Demodulation reference for high background rejection in 5G and 6G

ABSTRACT

Demodulation references are short messages exhibiting modulation levels of a modulation scheme, to assist the receiver in demodulating a message. Disclosed are short-form demodulation references suitable for pulse-amplitude modulation (PAM) messages in 5G and 6G. Each resource element of the short-form PAM demodulation reference provides two amplitude calibrations, one for each I or Q branch, from which the remaining amplitude levels of the modulation scheme can be readily calculated in real-time. The receiver can then demodulate a message by matching the branch amplitude values of each message element to the calibrated amplitude levels as determined from the demodulation reference. To indicate the start and end of the message, different configurations can be placed before and after the message. To mitigate high levels of background, a short single-symbol demodulation reference can be embedded in the message at multiple positions. Configurations are suitable for adoption as a demodulation standard.

PRIORITY CLAIMS AND RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/585,985, entitled “Short-Form Demodulation Reference for ImprovedReception in 5G and 6G”, filed Jan. 27, 2022, which claims the benefitof U.S. Provisional Patent Application Ser. No. 63/210,216, entitled“Low-Complexity Access and Machine-Type Communication in 5G”, filed Jun.14, 2021, and U.S. Provisional Patent Application Ser. No. 63/214,489,entitled “Low-Complexity Access and Machine-Type Communication in 5G”,filed Jun. 24, 2021, and U.S. Provisional Patent Application Ser. No.63/220,669, entitled “Low-Complexity Access and Machine-TypeCommunication in 5G”, filed Jul. 12, 2021, and U.S. Provisional PatentApplication Ser. No. 63/234,911, entitled “Short Demodulation Referencefor Improved Reception in 5G”, filed Aug. 19, 2021, and U.S. ProvisionalPatent Application Ser. No. 63/272,352, entitled “Sidelink V2V, V2X, andLow-Complexity IoT Communications in 5G and 6G”, filed Oct. 27, 2021,all of which are hereby incorporated by reference in their entireties.

FIELD OF THE INVENTION

Disclosed are procedures and formats for a short-form demodulationreference for low-complexity communication in a high-density 5G/6Gwireless network.

BACKGROUND OF THE INVENTION

A demodulation reference is a message that specifically exhibitsmodulation states of a modulation scheme (as opposed to data), andthereby assists the receiving entity in demodulating a subsequentmessage which is modulated according to the same modulation scheme. In5G and 6G, the primary demodulation reference is a DMRS (demodulationreference signal) which is configured according to one of a number ofpseudorandom sequences according to a complex formula. However, someuser devices may have difficulty processing such 5G and 6G requirements,or accommodating the bulky DMRS in their messages. In addition, thefluctuating interference background in high-density wirelessenvironments, such as a dense urban area or an automated factoryenvironment, may cause demodulation faults, resulting in missed calls,reduced reliability, and time-consuming retransmissions. What is neededis a demodulation reference configured for use by reduced-capabilitydevices and high-performance users alike, suitable for messaging in bothlow-density and high-density wireless traffic environments.

This Background is provided to introduce a brief context for the Summaryand Detailed Description that follow. This Background is not intended tobe an aid in determining the scope of the claimed subject matter nor beviewed as limiting the claimed subject matter to implementations thatsolve any or all of the disadvantages or problems presented above.

SUMMARY OF THE INVENTION

In a first aspect, there is a method for demodulating a messagecomprising message elements, each message element modulated according toa modulation scheme comprising pulse-amplitude modulation (“PAM”),wherein the modulation scheme comprises integer Namp amplitude levels,each amplitude level comprising one of the predetermined amplitudes ofthe modulation scheme, the method comprising: receiving a demodulationreference comprising integer Nref reference elements, Nref less than orequal to four, each reference element modulated according to themodulation scheme; determining, for each reference element, a referenceI-branch signal and a reference Q-branch signal at 90 degrees phaserelative to the reference I-branch signal; determining the Nampamplitude levels of the modulation scheme according to the referenceI-branch signals and the reference Q-branch signals; receiving themessage; for each message element, determining a message I-branchamplitude value and determining which of the Namp amplitude levels mostclosely matches the message I-branch amplitude value, and determining amessage Q-branch amplitude value and determining which of the Nampamplitude levels most closely matches the message Q-branch amplitudevalue; whereby each amplitude “level” is one of the amplitudes within amodulation scheme as provided by the reference I-branch and referenceQ-branch signals or combinations thereof, and each amplitude “value” isan amplitude of a particular message element as measured by a receiver.

In another aspect, there is non-transitory computer-readable media in awireless receiver containing instructions that when executed by acomputing environment cause a method to be performed, the methodcomprising: receiving a first demodulation reference comprising exactlyone reference element, the reference element modulated according to apulse-amplitude modulation (“PAM”) modulation scheme, the modulationscheme comprising integer Namp amplitude levels including a largestpositive amplitude level and a largest negative amplitude level;determining, according to the first demodulation reference, a firstreference I-branch signal and a first reference Q-branch signal at 90degrees phase relative to the first reference I-branch signal;determining the largest positive amplitude level according to onesignal, of the first reference I-branch and Q-branch signals;determining the largest negative amplitude level according to the othersignal, of the first reference I-branch and Q-branch signals; anddetermining at least one additional amplitude level by interpolatingbetween the largest positive and negative amplitude levels.

In another aspect, there is a wireless communication device configuredto: receive a demodulation reference comprising integer Nref resourceelements, Nref greater than 1 and less than 5, each resource elementmodulated according to a pulse-amplitude modulation (“PAM”) modulationscheme, the modulation scheme comprising integer Namp amplitude levels;determine, according to the Nref reference elements, Nref I-branchsignals and Nref Q-branch signals, the Q-branch signals offset by 90degrees in phase from the I-branch signals; determine, according to theNref I-branch signals and the Nref Q-branch signals, a plurality of theamplitude levels of the modulation scheme; determine, from the pluralityof the amplitude levels so determined, one or more additional amplitudelevels of the modulation scheme; receive a message comprising messageelements modulated according to the PAM modulation scheme, each messageelement comprising a message I-branch amplitude value and a messageQ-branch amplitude value; and compare each message I-branch amplitudevalue and each message Q-branch amplitude value to the Namp amplitudelevels of the modulation scheme, and therein determine which amplitudelevel, of the Namp amplitude levels of the modulation scheme, mostclosely matches each message I-branch amplitude value and each messageQ-branch amplitude value.

This Summary is provided to introduce a selection of concepts in asimplified form. The concepts are further described in the DetailedDescription section. Elements or steps other than those described inthis Summary are possible, and no element or step is necessarilyrequired. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended foruse as an aid in determining the scope of the claimed subject matter.The claimed subject matter is not limited to implementations that solveany or all disadvantages noted in any part of this disclosure.

These and other embodiments are described in further detail withreference to the figures and accompanying detailed description asprovided below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic sketch showing an exemplary embodiment of a phasechart for a 4-point short-form demodulation reference, according to someembodiments.

FIG. 1B is a schematic sketch showing an exemplary embodiment of amodulation table for a 4-point short-form demodulation reference,according to some embodiments.

FIG. 1C is a schematic sketch showing another exemplary embodiment of aphase chart for a 4-point short-form demodulation reference specifyingfour amplitude and four phase levels, according to some embodiments.

FIG. 1D is a schematic sketch showing another exemplary embodiment of amodulation table for a 4-point short-form demodulation referencespecifying four amplitude and four phase levels, according to someembodiments.

FIG. 1E is a schematic sketch showing an exemplary embodiment of a phasechart for a 4-point short-form demodulation reference for QPSK,according to some embodiments.

FIG. 1F is a schematic sketch showing an exemplary embodiment of amodulation table for a 4-point short-form demodulation reference forQPSK, according to some embodiments.

FIG. 2A is a sequence chart showing an exemplary embodiment of a processfor demodulating a message using a four-point short-form demodulationreference, according to some embodiments.

FIG. 2B is a flowchart showing an exemplary embodiment of a process fordemodulating a message using a four-point short-form demodulationreference, according to some embodiments.

FIG. 2C is a sequence chart showing another exemplary embodiment of aprocess for demodulating a message using a four-point short-formdemodulation reference, according to some embodiments.

FIG. 2D is a flowchart showing another exemplary embodiment of a processfor demodulating a message using a four-point short-form demodulationreference, according to some embodiments.

FIG. 3A is a schematic sketch showing an exemplary embodiment of a phasechart for a 2-point short-form demodulation reference, according to someembodiments.

FIG. 3B is a schematic sketch showing an exemplary embodiment of amodulation table for a 2-point short-form demodulation reference,according to some embodiments.

FIG. 3C is a schematic sketch showing another exemplary embodiment of aphase chart for a 2-point short-form demodulation reference specifyingtwo amplitude and phase levels, according to some embodiments.

FIG. 3D is a schematic sketch showing another exemplary embodiment of amodulation table for a 2-point short-form demodulation referencespecifying two amplitude and phase levels, according to someembodiments.

FIG. 3E is a schematic sketch showing an exemplary embodiment of a phasechart for a 2-point short-form demodulation reference for QPSK,according to some embodiments.

FIG. 3F is a schematic sketch showing an exemplary embodiment of amodulation table for a 2-point short-form demodulation reference forQPSK, according to some embodiments.

FIG. 4A is a sequence chart showing an exemplary embodiment of a processfor demodulating a message using a two-point short-form demodulationreference, according to some embodiments.

FIG. 4B is a flowchart showing an exemplary embodiment of a process fordemodulating a message using a two-point short-form demodulationreference, according to some embodiments.

FIG. 5A is a schematic sketch showing an exemplary embodiment of a phasechart for a 1-point short-form demodulation reference, according to someembodiments.

FIG. 5B is a schematic sketch showing an exemplary embodiment of amodulation table for a 1-point short-form demodulation reference,according to some embodiments.

FIG. 5C is a schematic sketch showing another exemplary embodiment of aphase chart for a 1-point short-form demodulation reference, accordingto some embodiments.

FIG. 5D is a schematic sketch showing another exemplary embodiment of amodulation table for a 1-point short-form demodulation reference,according to some embodiments.

FIG. 5E is a schematic sketch showing an exemplary embodiment of a phasechart for a 1-point short-form demodulation reference for QPSK,according to some embodiments.

FIG. 5F is a schematic sketch showing an exemplary embodiment of amodulation table for a 1-point short-form demodulation reference forQPSK, according to some embodiments.

FIG. 6A is a sequence chart showing an exemplary embodiment of a processfor demodulating a message using a one-point short-form demodulationreference, according to some embodiments.

FIG. 6B is a flowchart showing an exemplary embodiment of a process fordemodulating a message using a one-point short-form demodulationreference, according to some embodiments.

FIG. 7A is a schematic showing an exemplary embodiment of a wavemodulated using pulse-amplitude modulation, according to someembodiments.

FIG. 7B is a modulation table showing an exemplary embodiment of ademodulation scheme based on real and imaginary components, according tosome embodiments.

FIG. 8A is a schematic showing an exemplary embodiment of a resourcegrid with two-point short-form demodulation references interspersedwithin a message, according to some embodiments.

FIG. 8B is a schematic showing an exemplary embodiment of a resourcegrid with one-point short-form demodulation references interspersedwithin two messages, according to some embodiments.

Like reference numerals refer to like elements throughout.

DETAILED DESCRIPTION

5G and 6G technologies are designed for eMBB (enhanced Mobile Broadbandcommunications), URLLC (ultra reliable low latency communications), andmMTC (massive machine-type communication) generally involving largenumbers of user devices such as vehicles, mobile phones, self-propelledand robotic machines, portable and stationary computers, and many otheradvanced wireless instruments. However, many future IoT (internet ofthings) use cases are expected to involve simple, low-cost,reduced-capability MTC (machine-type communication) wireless devices.For example, a temperature sensor or a door alarm or a timer, amonginnumerable other task-based wireless products, may include a low-costprocessor such as a small microcontroller or an ASIC(application-specific integrated circuit) and may have minimal wirelesscommunication needs. Future automated factories are expected to uselarge numbers of such single-purpose wireless devices in a high-densitycommunication environment. Reduced-capability processors may havedifficulty performing complex 5G/6G procedures, which were developed forhighly competent devices that require high-performance communicationservices. Because both high-performance and reduced-capability devicesshare the same, limited electromagnetic spectrum, it would be tragic ifthe simpler machine-type applications are forced to develop a separatewireless technology, competing with 5G and 6G for bandwidth andlocations. A much more efficient solution is to include, in 5G and 6G, aset of simpler protocols and defaults appropriate for the low-cost,low-demand MTC devices. Experience with 4G has shown that incorporatingsuch flexibility into an already established radio-communicationtechnology is difficult. Therefore, if 5G and 6G are to makeaccommodation for reduced-capability systems in IoT applications,appropriate procedures and options should be incorporated as early inthe development as possible.

A related problem pertains to interference in high-density wirelessenvironments where thousands or millions of devices are in radio rangeof each other, such as an urban center or a highly automatedmanufacturing center. Background interference from the sea ofelectromagnetic signaling may cause frequent modulation distortions ineach message, degrading reliability, causing message faults,interruptions, delays, and missed calls, leading to severely limitednetwork throughput. Moreover, the retransmissions resulting from suchfaults will contribute further to the overall background, making theunderlying problem even worse. Interference is intrinsically bursty andfrequency-rich, that is, fluctuating rapidly in both time and frequency.Demodulation references can mitigate the interference problem byupdating the current amplitude and phase modulation levels to compensatefor the current interference effects, and may thereby assist indemodulating a subsequent message accurately despite interference.

The motivation behind the present disclosure is to provide ademodulation reference option, suitable for both high-performance andlow-cost devices, in sparse rural as well as dense urban/industrialwireless environments. Disclosed herein are short, low-complexitydemodulation references configured to enable user devices to modulateand demodulate messages in 5G and 6G networks. Systems and methodsdisclosed herein (the “systems” and “methods”, also occasionally termed“embodiments” or “arrangements”, generally according to presentprinciples) can provide urgently needed wireless communication protocolsto reduce messaging complexity and delays, facilitate low-complexitydemodulation, enable more frequent demodulation calibration in noisyenvironments, and provide readily available options to accommodatereduced-capability user devices, according to some embodiments.

Message demodulation includes receiving a demodulation reference and amessage, then determining the modulation state of each message elementaccording to amplitude and phase levels indicated in the demodulationreference. The message may be rendered in a numerical sequence that aprocessor can interpret. Standard modulation schemes in 5G and 6Ginclude BPSK (binary phase-shift keying), QPSK (quad phase-shiftkeying), 16QAM (quadrature amplitude modulation with 16 modulationstates), 64QAM, and 256QAM, although higher levels of QAM are possible.BPSK is rarely used. Most of the examples below relate to QPSK or 16QAM,with straightforward extension to the higher levels of modulation. QPSKis phase modulated at a constant amplitude, while the QAM schemes useboth amplitude and phase modulation. For example, QPSK has four phaselevels of modulation and only one amplitude level, whereas 16QAM hasfour phase and four amplitude levels. 64QAM has six amplitude and phaselevels, while 256QAM has eight amplitude and phase levels. The number ofamplitude levels in the modulation scheme may be termed “Namp”, and thenumber of phase levels “Nphase” herein. The modulation scheme thusincludes a number of “standard modulation states” of the modulationscheme, or simply “states” herein. The number of states, Nstates, isgenerally equal to the number of amplitude levels times the number ofphase levels. Adjacent amplitude levels of the modulation scheme areseparated by an “amplitude step”, and adjacent phase levels areseparated by a “phase step”. Phases are relative to the unmodulatedcarrier. “Nref” is the number of reference elements in the demodulationreference. A “calibration set” is a set of Namp amplitude levels andNphase phase levels, determined from the demodulation reference, whichcan be compared to each message element to demodulate the message.

Terms herein generally follow 3GPP (third generation partnershipproject) standards, but with clarification where needed to resolveambiguities. As used herein, “5G” represents fifth-generation, and “6G”sixth-generation, wireless technology in which a network (or cell or LANLocal Area Network or RAN Radio Access Network or the like) may includea base station (or gNB or generation-node-B or eNB or evolution-node-Bor AP Access Point) in signal communication with a plurality of userdevices (or UE or User Equipment or user nodes or terminals or wirelesstransmit-receive units) and operationally connected to a core network(CN) which handles non-radio tasks, such as administration, and isusually connected to a larger network such as the Internet. Thetime-frequency space is generally configured as a “resource grid”including a number of “resource elements”, each resource element being aspecific unit of time termed a “symbol period”, and a specific frequencyand bandwidth termed a “subcarrier” (or “subchannel” in somereferences). Symbol periods may be termed “OFDM symbols” (OrthogonalFrequency-Division Multiplexing) in references. The time domain may bedivided into ten-millisecond frames, one-millisecond subframes, and somenumber of slots, each slot including 14 symbol periods. The number ofslots per subframe ranges from 1 to 8 depending on the “numerology”selected. The frequency axis is divided into “resource blocks” (alsotermed “resource element groups” or “REG” or “channels” in references)including 12 subcarriers. Each subcarrier is at a slightly differentfrequency. The “numerology” of a resource grid corresponds to thesubcarrier spacing in the frequency domain. Subcarrier spacings of 15,30, 60, 120, and 240 kHz are defined in various numerologies. Eachsubcarrier can be independently modulated to convey message information.Thus a resource element, spanning a single symbol period in time and asingle subcarrier in frequency, is the smallest unit of a message.

In addition to the 3GPP terms, the following terms are also used herein.Each modulated resource element of a message is referred to as a“message element” in examples below, to avoid confusion over theambiguous term “symbol”. Likewise, each resource element of ademodulation reference is a “reference element” herein. A “messageamplitude value” is the amplitude modulation of a message element. A“reference amplitude value” is the amplitude modulation of a resourceelement of a demodulation reference. A “message phase value” is thephase modulation of a message resource element. A “reference phasevalue” is the phase modulation of a resource element of a demodulationreference. When the source of the element is unspecified or unambiguous,the terms may be shortened to “amplitude value” and “phase value”. A“calibration set” is a set of Namp amplitude levels and Nphase phaselevels specifying the modulation levels of the modulation scheme.Messages can be demodulated by comparing each message resource elementto the calibration set, thereby determining the amplitude level andphase level corresponding to the amplitude value and phase value of eachmessage element. A message may be configured “time-spanning” if itoccupies multiple sequential symbol periods at a single frequency, or“frequency-spanning” if it occupies multiple subcarriers at a singlesymbol period (as opposed to “TDD” time-division duplexing and “FDD”frequency-division duplexing, which refer to duplexing). A message is“unicast” if it is addressed to a specific recipient, and “broadcast” ifit includes no recipient address. Transmissions are “isotropic” if theyprovide roughly the same wave energy in all horizontal directions. Adevice “knows” something if it has the relevant information. A messageis “faulted” or “corrupted” if one or more bits of the message arealtered relative to the original message. “Receiver” is to beinterpreted broadly, as including connected processors and otherelectronics and related software/firmware configured to receive andprocess incoming wireless messages.

“Low-complexity” refers to devices and procedures necessary for wirelesscommunication, exclusive of devices and procedures that providehigh-performance communication. 5G/6G specifications include manyprocedures and requirements that greatly exceed those necessary forwireless communication, in order to provide high-performancecommunications at low latency and high reliability for users that demandit. Compared to scheduled and managed 5G/6G messaging, low-complexityprocedures generally require less computation and less signalprocessing. For example, low-complexity procedures may be tailored tominimize the number of separate operations required of a device per unitof time. 5G and 6G specifications include a very wide range of optionsand contingencies and versions and formats and types and modes for manyoperations, to achieve maximum flexibility. A low-complexityspecification may include defaults for each operation, and thosedefaults may be the simplest choices, or at least simpler than standard5G and 6G procedures. “Simpler” procedures generally require fewercomputation steps and/or smaller memory spaces than correspondingprocedures in standard 5G/6G. Computation steps may be measured infloating-point calculations, for example.

“Reduced-capability” refers to wireless devices that cannot comply with5G or 6G protocols, absent the systems and methods disclosed herein. Forexample, regular 5G and 6G user devices are required to receive a 5 MHzbandwidth in order to receive system information messages. Regular userdevices are required to perform high-speed signal processing such asdigitizing the received waveform, applying digital filtering or Fouriertransforming an incoming waveform, phase-dependent integrating atseveral GHz frequency, and separating closely-spaced subcarriers. Areduced-capability device, on the other hand, may not need the highperformance gained by such procedures, and may be incapable ofperforming them. A reduced-capability device may be able to receive anarrow-band wireless signal, demodulate the message, and interpret thecontent without further processing.

“High-density” wireless communication refers to cells where the numberof active transmitters per unit area challenges the ability of thenetwork to manage the traffic without degraded service. For example, ina built-up urban environment, a city block of 100×200 m² with 10-storeyapartment buildings, 100 m² per apartment at double occupancy, andconservatively assuming 5 wireless devices per person (phones, watches,fitness bands, and whatnot) plus 10 wireless devices per apartment(computers, smart appliances, doorbell cameras, temperature sensors, dogcollars, etc.), almost all of them being always-on devices, the activedevice density is then 40,000 devices per city block or about 2 devicesper square meter. The road space between blocks scarcely reduces thisload because it is typically filled with heavily-linked vehicles,traffic signals, wireless advertising signs, smart trash cans, andwhatever future inventors can devise. Basic physics says with confidencethat the electromagnetic background will be significant and fluctuating.

Communication in 5G and 6G generally takes place on abstract message“channels” (not to be confused with frequency channels) representingdifferent types of messages, embodied as a PDCCH and PUCCH (physicaldownlink and uplink control channels) for transmitting controlinformation, PDSCH and PUSCH (physical downlink and uplink sharedchannels) for transmitting data and other non-control information, PBCH(physical broadcast channel) for transmitting information to multipleuser devices, among other channels that may be in use. In addition, oneor more random access channels, termed “RACH” herein, also called PRACHin references, represents both abstract and physical random accesschannels, including potentially multiple random access channels in asingle cell, and configured for uplink and/or downlink, as detailedbelow. “CRC” (cyclic redundancy code) is an error-checking code. “RNTI”(radio network temporary identity) is a network-assigned user code.

5G and 6G references often use the same term for two different things.For example, “RACH” may refer to a random access message, the channel onwhich it is transmitted, or its assigned frequency or resource elements.“PBCH” may refer to a system information message or to thetime-frequency resources on which it appears. “Collision” may refer tosimultaneous interfering messages or to actual vehicle collisions.Disambiguation will be provided when necessary. Mathematical expressionsmay be sequentially ordered using parentheses, such as “A times (B plusC)” which means “add B to C, and then multiply that sum by A”.

For economic reasons as well as commercial feasibility, future IoTapplication developers will demand ways to transmit messages usingbandwidths and protocols appropriate to the simpler devices. It isimportant to provide such low-complexity options early in the 6Groll-out, while such flexibility can still be incorporated in the systemdesign.

The systems and methods disclosed herein include “short-formdemodulation references”. These are low-complexity demodulationreferences suitable for reduced-capability user devices as well ashigh-performance devices. In some embodiments, the low-complexitydemodulation references may be short messages, such as 1 or 2 or 3 or 4resource elements in length, and thus may be termed “short-form”demodulation references, due to their reduced Nref size relative to thedemodulation references of prior art. Examples focus on short-formdemodulation references of one or two or four resource elements inlength, termed one-point, two-point, and four-point short-formdemodulation references respectively, although other sizes such asNref=6 are possible. Each message element can be demodulated bydetermining the amplitude level and phase level at which that resourceelement has been modulated. Usually each amplitude level and phase levelof the modulation scheme has been assigned a number, so the demodulatedmessage may be represented by a sequence of such numbers, which aprocessor can then interpret to determine the message content.

In some embodiments, a short-form demodulation reference may explicitlyshow just a subset of the states of the modulation scheme, yet mayprovide sufficient information that a receiver can calculate theremaining modulation levels of the modulation scheme. Hence theprocessor can determine the remaining amplitude and phase levels of themodulation scheme, based on the subset of modulation levels explicitlyexhibited in the reference resource elements, plus conventions asdetailed below. In some embodiments, those calculations may involve onlylow-complexity calculations such as elementary logic and arithmetic. Thecalibration set can then be used for demodulating a message by comparingthe amplitude and phase of each message element to each level in thecalibration set. If a base station supports a low-complexity channel toaccommodate the lowered communication needs of simpler wireless devices,the short-form demodulation references disclosed herein may be readilyincorporated as the default demodulation reference for communications inthat channel. In addition, high-performance messaging on the scheduledand managed channels of 5G/6G may beneficially employ short-formdemodulation references for reduced latency, higher throughput, andimproved interference rejection in noisy environments, due to thereduced size and complexity of the short-form demodulation references.

In some embodiments, the receiver may know the size and format of ashort-form demodulation reference in advance of receiving it. Forexample, the receiver may already know the values of Namp, Nphase, Nref,and whether the exhibited amplitudes and phases represent the maximum orminimum levels, or other levels, of the modulation scheme. In otherembodiments, the receiver may not know the format of the demodulationreference in advance, in which case the receiver may employ proceduresdisclosed herein to determine the format by analysis of the short-formdemodulation reference, and to determine the remaining levels of themodulation scheme. In yet further embodiments, the receiver may knowsome of the listed format values in advance, and may determine othervalues by analysis of the short-form demodulation reference. In someembodiments, an amplitude ratio may be provided, equal to the minimumamplitude level of the modulation scheme divided by the maximumamplitude level. Additional information may be multiplexed into theprovided amplitude ratio, such as indicating whether the short-formdemodulation reference exhibits the minimum or maximum amplitude level,for example.

In some embodiments, the phase levels of the modulation scheme can becalculated from the phase levels exhibited in the short-formdemodulation reference, by “extrapolation” or “interpolation”.Extrapolation involves determining a phase step equal to the separationbetween adjacent phase levels of the modulation scheme, and thenrepeatedly adding the phase step to one of the exhibited phases, modulo360, and thereby determining all of the phase levels of the modulationscheme as well as Nphase. All phase values are modulo 360, that is,restricted to the range zero to 360 degrees. Phases are relative to theunmodulated carrier. It is immaterial whether the phase step is positiveor negative, or which of the exhibited phase values is used in theextrapolation, or in what order the various phase levels are found bythe extrapolation, since the levels in the calibration set can beordered according to phase value from low to high.

In some embodiments, interpolation may involve determining the maximumand minimum phase levels from the short-form demodulation reference, andthen calculating the Nphase-2 remaining intermediate phase levels byinterpolating between the maximum and minimum levels.

In some embodiments, the carrier phase of zero degrees is not used formodulation, and the minimum and maximum phase levels are configured toequally straddle the carrier phase, to avoid ambiguity and carriernoise. In that case, the minimum phase level of the modulation scheme isequal to one-half the phase step, and the maximum phase level is 360degrees minus one-half the phase step. This arrangement provides thatthe maximum and the minimum phase levels both remain as far as possiblefrom the carrier phase.

In some embodiments, one of the reference elements may bephase-modulated according to a first phase level, and another referenceelement may be phase-modulated according to the next higher phase levelof the modulation scheme, so that the two levels are separated by onephase step of the modulation scheme. The remaining phase levels of themodulation scheme can be found by determining a phase step “estimate” bysubtracting one of the exhibited phase values from the other, such asthe smallest non-zero difference between two of the exhibited phases inthe reference. The result is an estimate because the measured phasevalues generally include the effects of noise and interference. Thereceiver can then select the closest “standard” phase step value to theestimate. The standard phase step values are 180, 90, 60, and 45degrees, corresponding to BPSK, 16QAM or QPSK, 64QAM, and 256QAMrespectively. Then, the receiver can repeatedly add or subtract theselected standard phase step value to one of the phase values exhibitedin the short-form demodulation reference, to calculate the remainingphase levels of the modulation scheme. Selecting the standard phase stepalso determines Nphase as the number of phases in the range of zero to360 degrees. When prepared in this way, the resulting phase levels mayinclude the phase distortions of noise and interference as exhibited inwhichever reference phase value was used for the extrapolation. Theresulting phase levels may then be used to demodulate the elements of amessage that is subject to the same noise and interference as thereference elements. Since the message elements include the same noiseand interference effects as the reference elements, the effects of noiseand interference may be largely canceled in the demodulation, therebyenabling the receiver to correctly assign each message element'smodulation to the correct state of the modulation scheme, and therebyresulting in fewer message faults, according to some embodiments.

In some embodiments, the short-form demodulation reference may includethe minimum phase level only. If the receiver knows the phase of theunmodulated carrier, then the receiver can calculate the phase stepestimate equal to twice that minimum phase value, and can then selectthe closest standard phase step value, and can then find the other phaselevels by repeatedly adding the selected standard phase step to theminimum value. If the short-form demodulation reference includes themaximum phase level, the receiver can calculate the phase step estimateequal to twice the difference between that maximum value and 360degrees, then select the closest standard value, and then extrapolate tofind the other levels using the selected standard phase step value. Whencalculated in this way, each of the resulting phase levels may includethe effects of noise and interference, as indicated by the exhibitedphase value. Therefore the calculated phase levels, when used todemodulate a subsequent message that is subjected to the same noise andinterference, can largely cancel those effects, resulting in fewermessage faults despite noise and interference, according to someembodiments.

In some embodiments, the short-form demodulation reference may includetwo reference elements with phase modulations separated by two phasesteps, or other known number of phase steps. In that case, the receivercan determine the phase step by subtracting one of those referenceelements from the other.

In some embodiments, the receiver may know the modulation scheme inadvance, including Nphase, in which case the receiver can calculate thephase step as 360 degrees divided by Nphase, and can calculate thevarious phase levels of the modulation scheme, including noise andinterference effects, by adding the phase step repeatedly to one of theexhibited phase values, modulo 360.

In some embodiments, the maximum and minimum phase levels may beexhibited in the short-form demodulation reference. The receiver cancalculate the phase step estimate according to the phase differencebetween those two levels, modulo 360, because phase is a circularparameter, and hence a single phase step separates the maximum andminimum values. As mentioned, the receiver can then select the standardphase step closest to that estimate, and calculate the remaining phasemodulation levels of the modulation scheme by repeatedly adding orsubtracting the selected phase step to any one of the exhibited phasesin the short-form demodulation reference, modulo 360 degrees, and thenordering the levels by phase value. By these calculation examples, thephase step can be found as the phase difference between two of thereference elements, or alternatively twice the minimum phase (if thecarrier phase is known). Then, the receiver can determine Nphase equalto 360 degrees divided by the phase step, or equivalently 180 degreesdivided by the minimum phase. Then, the receiver can calculate eachphase level as the minimum phase times an odd integer. Alternatively,and equivalently, the receiver can calculate each phase level equal tothe minimum phase plus an integer times the phase step, among othermathematical relationships. In each case, the effects of noise andinterference may be included in each of the calculated phase levels, andtherefore the calculated phase levels can mitigate that same noise andinterference when used to demodulate the message elements. It isimmaterial which of the formulas listed above, or other equivalentformulas, are used by the receiver to determine the phase levels of themodulation scheme, so long as the reference elements provide enoughinformation to calculate the phase levels of the modulation scheme. Insome embodiments, the receiver knows, from convention or specificationsor system information or prior messaging for example, the format of theshort-form demodulation reference, including Nphase and Namp, how manyreference elements are in the short-form demodulation reference, and (ifnecessary) whether the carrier phase is included or avoided in themodulation phase levels. In other embodiments, the receiver does notknow the modulation scheme and/or the format of the short-formdemodulation reference, and may determine the necessary parameters frominformation provided in the short-form demodulation reference.

To consider some specific examples, QPSK and 16QAM each have four phaselevels, and the phase step is 90 degrees. The lowest phase level isnormally 45 degrees (relative to the carrier, and assuming nointerference). Thus the phase levels of the modulation scheme are 45,135, 225, and 315 degrees, and Nphase=4 levels for those modulationschemes. With the same assumptions, the minimum phase for BPSK is 90degrees, for 64QAM is 30 degrees, and for 256QAM is 22.5 degrees. Thephase step is twice these values. If interference is present, the phasesmay be shifted, in the reference elements and the message elements, dueto wave overlap. One purpose of the short-form demodulation reference isto enable the receiver to calibrate that distortion before demodulatingthe message, so that the phase values in the message elements can beassigned to the correct phase level of the modulation scheme, therebycompensating for current interference. In each case, a phase stepestimate can be determined as the magnitude of the difference in phasesof the exhibited levels, or as twice the minimum phase, or twice thedifference between 360 and the maximum phase, or as 360/Nphase,depending on which values are provided in the short-form demodulationreference. A standard phase step value closest to that estimate can thenbe selected. In each case, the complete set of phase levels in themodulation scheme can be determined by repeatedly adding the selectedstandard phase step value to any one of the phase levels exhibited inthe short-form demodulation reference, modulo 360 degrees.

In addition, the magnitude of the phase step can reveal the modulationscheme, if not already known to the receiver. For example, a phase stepof 180 degrees implies BPSK with Nphase=2, a phase step of 90 degreesimplies QPSK or 16QAM with Nphase=4, and a phase step of 60 degreesimplies 64QAM with Nphase=6, and a phase step of 45 degrees implies256QAM with Nphase=8. The method also applies to higher orders such as1024QAM with Nphase=10 and a phase step of 36 degrees, and highermodulation in the same way.

In some embodiments, the transmitter may be configured to modulate thereference elements and message elements by phase values that include thecarrier phase of zero degrees. Alternatively, the modulation may bebased on another starting value, or an unknown starting value. Forexample, the phase values of QPSK may include zero, 90, 180, and 270degrees. In that case, the receiver can calculate the phase step bysubtracting one of the exhibited phase values of the reference elementsminus another, or by dividing 360 by Nphase. The receiver can thendetermine the phase levels of the modulation scheme by repeatedly addingthe phase step to one of the exhibited phases in the short-formdemodulation reference, thereby determining the phase levels regardlessof whether the carrier phase is used as a phase level by thetransmitter.

In each of these cases, the phase values exhibited by the short-formdemodulation reference include the effects of current interference andnoise, and therefore provide a phase calibration for each phase levelthat compensates (or mitigates) the current noise and interference inthe message, and thereby enables the receiver to assign each phase valuein the message elements to the correct phase level of the modulationscheme despite noise and interference.

The amplitude modulation levels of the modulation scheme may also bedetermined from the amplitude levels exhibited in the short-formdemodulation reference. For QAM modulation schemes, the number ofamplitude levels Namp is equal to Nphase. For the PSK modulation schemes(BPSK and QPSK), Namp=1 since they are not amplitude modulated, and allmessage elements have the same amplitude. If the short-form demodulationreference includes multiple reference elements, all with the sameamplitude modulation, then the receiver can conclude that Namp=1, andthe modulation scheme is BPSK if the phase step is 180 degrees, or QPSKif the phase step is 90 degrees. For QAM-type modulation, the number ofamplitude levels is equal to the number of phase levels, which can bedetermined from the phases exhibited in the demodulation reference (ifnot already known to the receiver). The receiver can then determine thecomplete set of amplitude levels, and the specific QAM type, by firstcalculating the amplitude step, equal to the smallest non-zerodifference between any two of the amplitude values exhibited in theshort-form demodulation reference. The receiver can then repeatedly addthe amplitude step to the minimum amplitude level of the modulationscheme (if exhibited in the short-form demodulation reference) orrepeatedly subtract the amplitude step from the maximum amplitude levelof the modulation scheme (if exhibited in the short-form demodulationreference) until Namp amplitude levels have been determined, Nampequaling Nphase for QAM as mentioned. In other cases, the short-formdemodulation reference may include reference elements exhibiting theminimum and maximum amplitude levels, in which case the receiver candetermine the Namp-2 intermediate amplitude levels by interpolatingbetween the exhibited maximum and minimum amplitude values. In each ofthese cases, the amplitude values exhibited by the short-formdemodulation reference include the effects of current interference andnoise, and therefore provide an amplitude calibration for each amplitudelevel that compensates (or mitigates) the current noise and interferencein the message elements, and thereby enables the receiver to assign eachamplitude value in the message elements to the correct amplitude levelof the modulation scheme despite noise and interference.

In some embodiments, the short-form demodulation reference may includethe minimum amplitude in one reference element, and the minimumamplitude plus the amplitude step in another reference element. In thatcase, the remaining amplitude levels can be found by extrapolation, thatis, by determining the amplitude step by subtracting one referenceelement amplitude value from the other, and then repeatedly adding theamplitude step to either of those exhibited values until Namp amplitudelevels are obtained.

In some embodiments, the short-form demodulation reference may exhibitthe maximum amplitude level and the next-lower level, which is oneamplitude step lower than the maximum. In that case, the amplitude stepcan be calculated by subtracting one of the reference amplitudes fromthe other, thereby obtaining the amplitude step, and then the remainingamplitude levels can be determined by repeatedly subtracting theamplitude step from either of the exhibited levels.

In some embodiments, the short-form demodulation reference may exhibitboth the minimum and maximum amplitude levels, in which case theintermediate levels can be found by interpolation. In general,interpolation is more accurate than extrapolation and less sensitive tomeasurement uncertainties; hence, the version with maximum and minimummodulation levels explicitly provided may be preferred. In each case,the receiver is expected to know whether the minimum or maximumamplitude level is exhibited in the short-form demodulation reference,so that the receiver can add or subtract or interpolate as appropriate.Conventions may be established determining such a default format.

In some embodiments of the short-form demodulation reference, an“amplitude ratio” may be known to the receiver. The amplitude ratio maybe equal to the minimum amplitude level divided by the maximum amplitudelevel of the modulation scheme (other versions discussed below). Thusthe amplitude ratio is 1.0 for PSK modulation schemes such as BPSK orQPSK, since they have no amplitude modulation. For QAM modulations, theamplitude ratio is less than 1. All of the amplitude levels of themodulation scheme can then be determined from the amplitude valuesexhibited in the short-form demodulation reference. If the exhibitedamplitude values of the short-form demodulation reference are all equal(within measurement error), then Namp=1. If the reference amplitudevalues are not all (substantially) equal, then the maximum and minimumamplitude levels of the modulation scheme can be calculated from theprovided amplitude ratio, and then the remaining amplitude levels can bedetermined by interpolation between the maximum and minimum amplitudevalues so calculated. “Substantially equal” in this context impliesequal to within less than one-half of an amplitude step.

For example, in case the short-form demodulation reference includes asingle reference element only, and the amplitude ratio has been providedseparately, and if the single reference element exhibits the minimumamplitude, then he receiver can calculate the maximum amplitude bydividing the minimum amplitude value by the amplitude ratio. On theother hand, if the exhibited amplitude is the maximum, then the minimumcan be found by multiplying that value by the amplitude ratio. For thecase of a one-point short-form demodulation reference, the receivingentity is expected to know (by convention or default or unicast messageor system information broadcast, for example) the amplitude ratio, andwhether the exhibited amplitude represents the minimum or maximumamplitude level. In either case, after calculating the opposite level bymultiplying or dividing the exhibited amplitude by the amplitude ratio,the receiver can calculate all of the remaining amplitude levels byinterpolation.

In another embodiment, the amplitude ratio equals the maximum amplitudelevel divided by the minimum amplitude level of the modulation scheme,and thus is greater than or equal to 1. In that case, the receiver candetermine the minimum amplitude level by dividing an exhibited maximumamplitude level by the amplitude ratio, or can determine the maximumamplitude level by multiplying an exhibited minimum amplitude level bythe amplitude ratio. The receiver is expected to know whether theamplitude ratio is the minimum divided by the maximum, or the inverse.

In another embodiment, a short-form demodulation reference may have justone reference element, and the receiver may not know whether theexhibited amplitude is the maximum or minimum, and yet may stillcalculate all of the amplitude levels of the modulation scheme. To doso, a modified amplitude ratio may be provided, in which the modifiedamplitude ratio is configured to indicate whether the maximum or minimumis exhibited in the single reference element. For example, the amplituderatio may be set to equal the maximum divided by the minimum amplitude(that is, greater than 1) when the exhibited amplitude is the minimum,and the modified amplitude ratio may be set equal to the minimum dividedby the maximum (that is, less than 1) when the exhibited amplitude isthe maximum. The receiver then does not need to know whether the maximumor minimum amplitude level is shown. Instead, the receiver can multiplythe exhibited amplitude value by the modified amplitude ratio in eithercase, and thereby obtain a second amplitude value. The receiver can thencalculate the intermediate amplitude values by interpolation betweenthose two values. Although the receiver does not know whether theexhibited amplitude is the maximum or minimum, nevertheless the receivercan calculate the intermediate levels by interpolating between theexhibited amplitude and the second amplitude. In other words, themodified amplitude ratio is configured to automatically accommodateeither possibility.

Regardless of the order in which the amplitude levels are calculated,the resulting amplitude levels may be re-ordered from minimum to maximumin the calibration set, and numbered accordingly.

The foregoing descriptions are based on classical amplitude modulationmultiplexed with classical phase modulation. However, in someembodiments, the demodulation reference and the message elements may bemodulated by pulse-amplitude modulation (PAM), in which twoamplitude-modulated signals are added with a 90-degree phase offsetbetween them. Upon receipt, the demodulator then picks out the “real”(zero offset) and “imaginary” (90-degree offset) signals for each of thereference elements and message elements. The two phase modulations arealso sometimes called the “I” or in-phase component and the “Q” orquadrature component. The receiver then prepares a “constellation” ofmodulation states from the measured real and imaginary values of thereference elements, each state having a particular real amplitude and aparticular imaginary amplitude. Negative amplitude values correspond toa 180-degree phase shift. The receiver then demodulates the messageelements by comparing their real and imaginary values to the real andimaginary levels of the constellation, and thereby determines themodulation state of each message element, as desired. For example, 16QAMwith PAM modulation has four real amplitudes and four imaginaryamplitudes, which are combined in each message element to yield 16states overall. The constellation of PAM is equivalent to thecalibration set of regular amplitude-phase modulation. The extrapolationand interpolation methods described above are straightforwardlyapplicable to the real-imaginary modulation states of PAM. Many othermodulation technologies and schemes exist. As long as the modulationscheme involves modulating the phase and (optionally) the amplitude ofan electromagnetic wave, it is immaterial which modulation technology isemployed. The principles disclosed herein may apply to each of thesemodulation technologies, as will be apparent to artisans with ordinaryskill in the art after reading the present disclosure.

Numerous formats of the short-form demodulation reference are envisionedand disclosed. The short-form demodulation reference may include asingle reference element, two reference elements, four referenceelements, or three or six or any number of reference elements. Theshort-form demodulation reference may exhibit the maximum or minimumphase level, and/or the maximum or minimum amplitude level, of themodulation scheme. The short-form demodulation reference may include tworeference elements that differ in phase by one phase step and/or thatdiffer in amplitude by one amplitude step, or other known number ofamplitude or phase steps. Separate information may be provided such asan amplitude ratio and/or an indication that the short-form demodulationreference includes a minimum or maximum amplitude and/or Namp and/orNphase and/or the modulation type. Such information may be provided by aprevious message, or by convention, or by a default for low-complexityprotocols, or otherwise. The receiver is expected to have sufficientinformation to be able to calculate any remaining levels from theexhibited modulation states, and thereby to complete the calibrationset. Such calculations may include basic arithmetic and logic,consistent with the low-complexity methods presented herein. Due to themany possible versions listed and envisioned, differing in format butotherwise equivalent, it would be helpful for a wireless standardscommittee to declare one of the short-form demodulation versions to be adefault standard.

Turning now to the figures, in a first example, the systems and methodsinclude a four-point short-form demodulation reference with a length offour reference elements.

FIG. 1A is a phase chart showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a 4-point short-formdemodulation reference, according to some embodiments. A phase chart isa schematic representation of the states of a modulation scheme, in apolar coordinate system representing phase azimuthally and amplituderadially. As depicted in this non-limiting example, the large circles100 represent the amplitude levels of the modulation scheme, and some ofthe states of the modulation scheme are shown as points such as 101 and102. The amplitude of a state 101 is shown as the radius 104. The phaseof a state 101 is shown as the angle 103 relative to the horizontal axis(going counter-clockwise). The horizontal axis represents zero degrees,or unmodulated carrier. The number of amplitude levels Namp is thenumber of the large circles 100, and the number of phase levels Nphaseequals the number of angles 103 of the states. For clarity, not all ofthe states of the modulation scheme are shown. The modulation scheme is16QAM in this case, with Namp=4 and Nphase=4.

The states of the depicted four-point demodulation reference areconfigured to explicitly exhibit four amplitude levels 100 and fourphase levels 103. If the modulation scheme is 16QAM or QPSK, those fourstates thereby specify all of the amplitude and phase levels of themodulation scheme, and no interpolation or extrapolation is needed. Ifthe modulation scheme is higher, such as 256QAM, then the remainingamplitude and phase levels of the modulation scheme may be calculatedfrom the exhibited ones by interpolation or extrapolation as describedabove.

As depicted in this non-limiting example of a four-point short-formdemodulation reference, the first state 101 is phase-modulated at theminimum phase level, and the second state 102 is phase-modulated at theminimum phase plus a phase step. The phase step estimate can thereforebe calculated by subtracting the first phase value 101 from the secondphase value 102 or vice versa (the sign of the phase step beingimmaterial, since phase is a circular parameter). Alternatively, thephase step estimate can be calculated by doubling the minimum phasevalue as exhibited in point 101, assuming that the minimum phase and themaximum phase are equally spaced from zero degrees. In this example, theminimum phase point 101 and the maximum phase point 102 are both spacedapart from the carrier by the same amount, which is ±45 degrees for16QAM. Thus the minimum phase is 45 degrees and the phase step is 90degrees for 16QAM, as shown. The number of phase states is 360 degreesdivided by the phase step, or equivalently 180 degrees divided by theminimum phase. By either method, Nphase equals 4 in the depicted case.The measured phase levels may differ from the ideal values due to noiseand interference. However, based on the estimated phase step from themeasured phase values, the receiver can then select the closest“standard” phase step corresponding to a standard modulation scheme suchas 16QAM. In the depicted example, the phase difference between adjacentphase levels is 90 degrees, and therefore the modulation scheme iseither 16QAM or QPSK. Four amplitude levels are indicated, so it cannotbe QPSK, and therefore the scheme must be 16QAM.

The short-form demodulation reference can also enable the receiver todetermine all of the amplitude levels of the modulation scheme. In thedepicted modulation scheme, an integer number Namp of amplitude levels(specifically four amplitude levels) are indicated by the four largecircles 100 of varying radius. If the modulation scheme is 16QAM, as inthe present case, then the four amplitude values exhibited in theshort-form demodulation reference include all of the amplitude levels ofthe modulation scheme. If a higher order of modulation is involved, andthe short-form demodulation reference exhibits the maximum and minimumamplitude levels of the modulation scheme, then the receiver cancalculate the Namp-2 intervening amplitude levels by interpolationbetween the minimum and maximum amplitude levels. The receiver knowsNamp at that time either by convention or by the phase levels asdescribed above.

In the figure, the four depicted states are the reference elements of ashort-form demodulation reference that exhibits four amplitude levelsincluding a maximum amplitude (for point 101) and a minimum amplitude(point 102), plus two intermediate points not labeled. The points alsoexhibit the maximum, minimum, and two intermediate phases. In this case,the four-point short-form demodulation reference exhibits all fouramplitude levels and all four phase levels in 16QAM, and therefore nointerpolation or extrapolation or other calculation is needed to fill inthe levels of the calibration set. All of the amplitude levels and phaselevels of the modulation scheme are explicitly exhibited by theshort-form demodulation reference as shown, and those levels correspondto the complete calibration set for 16QAM. The levels explicitlyexhibited in the depicted short-form demodulation reference aretherefore sufficient to enable a receiver to determine the completecalibration set, without the need for interpolation or extrapolation, inthis case.

Higher levels of modulation, such as 256QAM, can also be demodulatedaccording to a four-point short-form demodulation reference, bycalculating the intermediate amplitude and phase levels by interpolationor extrapolation as described above.

A method for demodulating message elements may include calculating acalibration set that includes the amplitude and phase modulation levelsof a modulation scheme, based at least in part on the exhibitedamplitude and phase values of reference elements in a short-formdemodulation reference, wherein elementary calculations are sufficientto determine amplitude and phase levels not explicitly represented inthe reference elements. To demodulate a message, the receiver cancompare the amplitude and phase modulation values of each messageelement to the levels in the calibration set, and select theclosest-matching levels.

A method for demodulating a message modulated with a modulation schemeof higher order, such as 256QAM with 8 phase levels and 8 amplitudelevels, using a four-point short-form demodulation reference, mayinclude determining amplitude and phase levels of the modulation schemefrom the phase and amplitude levels exhibited by the short-formdemodulation reference, which is a subset of the amplitude and phaselevels of the modulation scheme. For example, if the minimum and maximumamplitude levels are exhibited in the short-form demodulation reference,the remaining amplitude levels can be found by interpolating between theminimum and maximum amplitude values, thus totaling Namp levels.Alternatively, the amplitude levels may be found by calculating theamplitude step from the exhibited amplitude levels, and then repeatedlyadding the amplitude step to one of the amplitudes provided. Likewise,the remaining phase levels may be found by interpolating between themaximum and minimum phase values if provided, or by repeatedly addingthe phase step to one of the phase values exhibited in the short-formdemodulation reference.

FIG. 1B is a modulation table showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a four-point short-formdemodulation reference such as that of FIG. 1A, according to someembodiments. A modulation table is a graphic showing the modulationstates of a modulation scheme, with phase shown horizontally andamplitude shown vertically. As depicted in this non-limiting example,the modulation table shows the sixteen states of 16QAM as circles 110,and the four stippled states correspond to the four states indicated inFIG. 1A. The state 111 exhibits the maximum amplitude and the lowestphase, corresponding to 101 in the previous figure, and state 112exhibits the minimum amplitude with the second phase level,corresponding to 102. These are followed by two more states withintermediate amplitude and phase values. Thus FIGS. 1A and 1B containthe same information in different forms.

FIG. 1C is a phase chart showing another exemplary embodiment of a shortlow-complexity demodulation reference such as a 4-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the four points span the four amplitudelevels and four phase levels of 16QAM in a particular order. Amplitudelevels are shown as large circles 120. Unlike the previous example, thepoints are sequenced through the amplitude and phase levels in amonotonic fashion. The first point 121 exhibits the minimum amplitudelevel and the minimum phase level. The second point 122 has thenext-larger amplitude level and the next-larger phase level, and theremaining points continue the same pattern. In this case, the modulationscheme is 16QAM with four amplitude and four phase levels. Thefour-point short-form demodulation reference can explicitly exhibit allof the amplitude and phase levels of the modulation scheme, therebyproviding a complete calibration set explicitly, as mentioned. A messagemay be demodulated by comparing the various amplitude and phase levelsof the short-form demodulation reference to the amplitude and phasevalues of the message elements.

FIG. 1D is a modulation table showing an exemplary embodiment of alow-complexity demodulation reference such as a four-point short-formdemodulation reference such as that of FIG. 1C, according to someembodiments. As depicted in this non-limiting example, the modulationstates (of 16QAM in this case) are shown as circles 130 in amplitude andphase, and four stippled states (131 and 132 labeled) represent the fourreference elements of the short-form demodulation reference,corresponding to the points of FIG. 1C. As shown, the short-formdemodulation reference elements exhibit the minimum amplitude with theminimum phase, then the next-higher amplitude and phase levels, followedby the remaining states in ascending order.

FIG. 1E is a phase chart showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a 4-point short-formdemodulation reference for QPSK, according to some embodiments. Asdepicted in this non-limiting example, the four points lie on a singleamplitude circle 160, since QPSK has a single amplitude (in other words,QPSK is not amplitude-modulated). The first point 161 has minimum phase,the next point 162 has the next-higher phase, and so forth for fourpoints. An advantage of using a four-point short-form demodulationreference for the four-point QPSK scheme may be that all of themodulation states can be explicitly provided in the short-formdemodulation reference, so that the message elements can be demodulatedby directly comparing with the reference elements of the short-formdemodulation reference without interpolation, which may be easier forreduced-capability devices.

FIG. 1F is a modulation table showing an exemplary embodiment of alow-complexity demodulation reference such as a four-point short-formdemodulation reference such as that of FIG. 1E, according to someembodiments. As depicted in this non-limiting example, the four statesof QPSK are all stippled, indicating that they all appear in theshort-form demodulation reference elements. The first state 171corresponds to 161 and the second state 172 corresponds to 162.

An advantage of providing a four-point short-form demodulation referencesuch as that of FIG. 1A or 1B or 1C or 1D or 1E or 1F may be that thephase and amplitude values provided in the short-form demodulationreference may be used to demodulate the message elements. Anotheradvantage may be that the provided amplitude values can explicitlyexhibit all of the modulation scheme amplitude and phase levels directly(as in 16QAM), or can be interpolated to calculate all of the amplitudeand phase levels (as in 256QAM). Another advantage may be that the phaselevels of a modulation scheme may be calculated by determining a phasestep estimate from the reference elements, selecting the closeststandard value, and repeatedly adding the selected phase step to one ofthe exhibited phases, modulo 360, thereby determining all of the phaselevels of the modulation scheme. Another advantage may be that theamplitude levels of the modulation scheme may be determined byinterpolating between maximum and minimum amplitudes provided in theshort-form demodulation reference, or by calculating an amplitude stepand repeatedly adding or subtracting the amplitude step to the exhibitedamplitudes. Another advantage may be that the four-point short-formdemodulation reference is short, only four reference elements, and thusmay be appended or prepended to other messages, or interspersed withinlonger messages, to provide frequent updates of the specific modulationlevels used in an accompanying message, including effects of localinterference, if any. Alternatively, the short-form demodulationreference may be supplied separately from a message, such asperiodically, such as in the first four subcarriers of the first uplinkor downlink symbol period of each slot, or the first four symbol periodsof a single subcarrier in each slot, for example. Another advantage maybe that the four-point short-form demodulation reference may include themaximum and minimum amplitudes, in which case there may be no need toextrapolate amplitude values beyond those explicitly exhibited in theshort-form demodulation reference. Another advantage may be that thephase levels provided in the reference may include the minimum phaselevel and the next-higher phase level, or the maximum phase and themaximum phase minus the phase step, or separated by twice the phasestep, or other like combinations. In each case, all of the amplitude andphase levels of the modulated message may be identified by interpolationand extrapolation, and the message may thereby be demodulated, so longas the receiving entity knows which type of short-form demodulationreference is employed. Another advantage may be that distortions, inamplitude or phase or both, due to noise or interference, may beincluded in the amplitude and phase values of the reference elements,and therefore those distortions may be canceled when the receivedreference values are used to demodulate a subsequent message.

Another advantage may be that the procedures of FIG. 1A or 1B or 1C or1D or 1E or 1F may be implemented as a software (or firmware) update,without requiring new hardware development, and therefore may beimplemented at low cost, according to some embodiments. The proceduresof FIG. 1A or 1B or 1C or 1D or 1E or 1F may be implemented as a systemor apparatus, a method, or instructions in non-transientcomputer-readable media for causing a computing environment, such as auser device, a base station, or other signally coupled component of awireless network, to implement the procedure. Another advantage may bethat the depicted low-complexity procedures may be compatible withdevices that may have difficulty complying with prior-art registrationprocedures. Other advantages may be apparent to one of ordinary skill inthe art, given this teaching. The advantages listed in this paragraphare also true for other lists of advantages presented for otherembodiments described below.

FIG. 2A is a sequence chart showing an exemplary embodiment of alow-complexity procedure for demodulating a message using a short-formdemodulation reference, according to some embodiments. Actions andevents of a receiver are shown on the first line, then actions or eventsof a processor connected to the receiver on the second line, and aresult or processor output is shown on the last line. Although messagesare usually shown time-spanning in sequence charts for clarity, in manycases the messages may be transmitted as frequency-spanning. Arrows showtiming or information flow. In this case, the receiver does not know thespecific format of the short-form demodulation reference (“Demod”), andtherefore must determine Namp and Nphase from the values exhibited inthe short-form demodulation reference. As depicted in this non-limitingexample, the demodulation reference is a four-point short-formdemodulation reference 201, followed by an optional gap 206, and amessage 202 which is to be demodulated, with little marks demarking eachof the message elements. The gap 206 may be one symbol period or more,and may include zero transmission, or transmission with an amplitudebelow the lowest amplitude level of the modulation scheme, orunmodulated carrier (at the subcarrier frequency), or othercharacteristic signal not resembling the data. The position of the gap206 may thereby indicate the length of the demodulation reference 201,and may also indicate the starting point of the message 202, which maybe helpful to the receiver if the format of the short-form demodulationreference 201 is not already known. The gap 206 thereby indicates thatthe short-form demodulation reference 201 is provided in the resourceelements preceding the gap 206, and the message to be demodulated 202 isprovided after the gap 206. The processor may analyze the referenceelements of the four-point short-form demodulation reference and maythereby determine an amplitude and phase calibration set 203, based onthe amplitude and phase values of the demodulation reference 201, andalso using amplitude interpolation or extrapolation, and phaseinterpolation or extrapolation, as needed to calculate any remaininglevels that are not explicitly provided in the short-form demodulationreference 201.

Then, the processor may analyze each resource element of the message202, by comparing the amplitude of each message element 202 to thecalibration set 203, and comparing the phase of each message element 202to the calibration set 203, and may thereby assign amplitude and phasemodulation levels 204 to each of the message elements.

The modulation levels may be represented numerically. For example, eachamplitude and phase level in the calibration set 203 may be assigned abinary code. In 16QAM with four amplitude levels and four phase levels,the code may be a two-bit binary code, such as 00 for the lowestamplitude level, 01 and 10 for intermediate levels, and 11 for thehighest level. Likewise the four phase modulation levels can berepresented by 00 for the lowest and 11 for the highest phase. Themodulation state of each message element 202 may then be represented bya 4-bit code indicating the specific amplitude level and phase level204. The 4-bit code may show the amplitude code followed by the phasecode, for each message element. For example, a message element modulatedwith the lowest amplitude level and the highest phase level would be0011. The message 202 can then be represented by a series 205 of binarybits containing the message information.

The bit-level representation generally depends on the modulation scheme.BPSK represents one bit per message element, QPSK has 2 bits per messageelement, 16QAM has 4 bits per message element, 64QAM requires 6 bits permessage element, and 256QAM would need 8 bits per message element.

FIG. 2B is a flowchart showing an exemplary embodiment of alow-complexity procedure for using a short-form demodulation reference,according to some embodiments. As depicted in this non-limiting example,a receiver does not know initially the format of the short-formdemodulation reference. Therefore, the receiver first determines thephase step from the phase values in the short-form demodulationreference and determines Nphase. The receiver can then refer to theamplitudes in the short-form demodulation reference and determine thatthe amplitude levels are not all equal to each other, which indicatesthat the modulation scheme is a QAM type. The receiver therefore setsNamp equal to Nphase, and thereby determines the modulation schemespecifically. The receiver then performs calculations if necessary todetermine any remaining phase and amplitude levels, stores them in acalibration set in a processor memory, and then compares the messageelements to the modulation levels so determined.

At 250, a receiving entity receives a four-point short-form demodulationreference and, at 251, measures the amplitude values and phase values ofeach of its four reference elements. At 252, the receiver determines thephase step estimate by subtracting one of the exhibited phase levelsfrom another, then selects the closest standard phase step value, anddetermines Nphase by dividing 360 by the selected phase step value.Alternatively, and more simply in this case, the receiver may accept thephase levels exhibited in the demodulation reference as the phase levelsof the modulation scheme, interpolating if necessary to fill in anyintervening levels. The receiver also compares the various amplitudevalues in the short-form demodulation reference and determines whetherNamp=1 or Namp=Nphase. At 253, the receiver determines whether themodulation is higher than 16QAM, according to Nphase as determined. Ifthe modulation is higher than 16QAM, such as 64QAM or 256QAM, then at254 the receiver calculates the remaining amplitude and phase levelsfrom those explicitly exhibited in the short-form demodulation referenceelements, by interpolating between the maximum and minimum amplitudevalues or by extrapolating with the amplitude step, and by interpolatingor extrapolating the phase values, as described above. At 255, theamplitude and phase modulation values from the short-form demodulationreference elements and, if applicable, from the calculations, areaccumulated as a calibration set which includes all of the amplitude andphase levels of the modulation scheme.

At 256 (if not sooner), the message to be demodulated is received. At257, each message element is compared to the amplitude and phasemodulation levels in the calibration set. The amplitude value of eachmessage element is thereby assigned a specific amplitude modulationlevel, and the phase value of each message element is assigned aspecific phase modulation level, by comparing to the calibrated levels.At 258, a binary representation of the message is prepared byconcatenating the numbers associated with each amplitude and phase levelof each message element, and is done at 259.

An advantage of providing a four-point short-form demodulation referencemay be that it is short, just four reference elements. Another advantagemay be that four modulation states in phase and amplitude can beexplicitly provided, thereby enabling direct demodulation of QPSK or16QAM without interpolation or extrapolation, in some embodiments.Another advantage may be that higher modulation schemes such as 64QAM or256QAM may be demodulated, using interpolation or extrapolation toderive the remaining levels from the explicitly provided levels. Anotheradvantage may be that distortions, in amplitude or phase or both, due tonoise or interference, may be included in the amplitude and phase valuesof the reference elements, and therefore those distortions may becanceled when the received reference values are used to demodulate asubsequent message.

FIG. 2C is a sequence chart showing another exemplary embodiment of aprocess for demodulating a message using a four-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, a receiver initially obtains information 220about the format of a 4-point short-form demodulation reference(“Demod”) 221, and therefore can proceed to fill in the calibration set223 more directly than in the previous example, using the known format(including Namp, Nphase, whether the maximum or minimum amplitude andphase values are exhibited, and like information). The receiver alsoreceives the message 222 and, comparing each message element's phase andamplitude values to the corresponding values in the calibration set 223,determines the amplitude and phase levels 223 of the modulation schemefor each message element. The receiver then converts the amplitude andphase levels (A&P) 224 to the corresponding binary code 225, and passesthe demodulated message to a processor for interpretation.

FIG. 2D is a flowchart showing another exemplary embodiment of a processfor demodulating a message using a four-point short-form demodulationreference, according to some embodiments. As depicted in thisnon-limiting example, a receiver initially obtains information about theformat of a subsequent four-point short-form demodulation reference at260. At 261, the receiver receives the four-point short-formdemodulation reference, and at 262 measures the amplitude and phasevalues of each reference element. At 263, the receiver uses the knownformat of the short-form demodulation reference to calculate theremaining amplitude and phase levels of the modulation scheme notexhibited in the reference elements, and thereby fills in thecalibration set with all of the amplitude and phase levels of themodulation scheme at 264. At 265 (if not sooner) the receiver receivesthe message and, at 266, compares each message element's amplitude andphase values to those of the calibration set, thereby determining whichlevel is a closest match to each message element. At 267, the receiverconverts those amplitude and phase levels for each message element tonumbers that a processor can interpret, and is done at 268.

The systems and methods further include a two-point short-formdemodulation reference with a length of two reference elements, as inthe following examples.

FIG. 3A is a phase chart showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a two-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the short-form demodulation referenceincludes two points representing two reference elements with particularmodulations. The amplitude levels are indicated as circles 300. Thedemodulation reference includes a first reference element 301 modulatedwith a maximum amplitude and a minimum phase (45 degrees in this case),and a second reference element 302 with the minimum amplitude value andmaximum phase. The phase step estimate can be calculated as the phasedifference between the two points 301-302, or by doubling the minimumphase as exhibited by point 301, or by doubling the difference between360 degrees and the phase of the other point 302, among many other waysto determine the phase step estimate. In each case, the receiver selectsa standard phase step value that is closest to the phase step estimatederived from the measured values of the reference elements. For the caseshown, the selected standard phase step value is 90 degrees and themodulation scheme is 16QAM. The short-form demodulation referencethereby exhibits the maximum and minimum amplitude levels and themaximum and minimum phase levels of the modulation scheme. The number ofphase levels can be determined from the phase step (specifically, 360degrees divided by the phase step), and the intermediate phase levelscan be calculated by interpolation between the minimum and maximumphases. The number of amplitude levels is 1 if the minimum and maximumamplitudes are the same, or substantially the same (such as, withinexpected measurement uncertainties), and Namp is equal to the number ofphase levels otherwise. In the depicted case, the amplitude levels ofthe two points 301-302 are not equal, and therefore the modulationscheme cannot be PSK, and therefore is QAM at some order. The order is16QAM here since, for QAM schemes, the number of amplitude levels isequal to the number of phase levels, or Namp=Nphase, and for 16QAM thephase step is 90 degrees. The various amplitude levels of the modulationscheme may be calculated by interpolation between the minimum andmaximum amplitudes explicitly exhibited in the short-form demodulationreference. The set of amplitude and phase levels thus determinedconstitutes the calibration set, and the message elements, which weremodulated according to the same modulation scheme, can be demodulated bycomparison with the amplitude levels of the calibration set.

FIG. 3B is a modulation table showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a 2-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the table shows valid modulation states 310of, in this case, 16QAM, with phase horizontally and amplitudevertically. Two states 311 and 312 are stippled, corresponding to thestates 301, 302 of FIG. 3A. The state 311 represents the first referenceelement of the two-point short-form demodulation reference, with themaximum amplitude and the minimum phase, while the second stippled point312 has the minimum amplitude and the maximum phase. The phasedifference between the two points 311-312 (or 360 minus the difference,depending on the order of the points) thereby indicates the phase stepestimate, and the remaining phase levels can be found by selecting theclosest standard phase step and repeatedly extrapolating from either ofthe points 311-312 by the selected phase step, modulo 360, or byinterpolating between the maximum and minimum phase values exhibited.The remaining amplitude levels can be found by linearly interpolatingbetween the amplitude values of the two reference elements 311-312.Hence the complete calibration set of amplitude and phase levels of themodulation scheme can be found from the two-point short-formdemodulation reference, if the receiving entity knows the type andformat of the short-form demodulation reference. The message elementsmay then be demodulated by comparing each message element to thecalibration set. The two-point short-form demodulation referenceprovides sufficient information to generate the complete calibrationset, if the reference elements include the maximum and minimum amplitudelevels, or if they differ by one amplitude step or a known number ofamplitude steps, and if the reference phases include the maximum andminimum phases, or they differ by one phase step or a known number ofphase steps. In each case, the remaining amplitude and phase levels canbe calculated by interpolation and/or extrapolation, as described.

For simplicity and standardization, a default demodulation referenceformat may advantageously be selected, for example by a wirelessstandards committee. The default short-form demodulation reference maythen be used in a wide range of applications and users. The short-formdemodulation reference of FIGS. 3A and 3B would be an advantageouschoice because all of the remaining amplitude and phase levels can bereadily calculated using only interpolation between the points provided,and the same methods apply to all PSK and QAM modulation schemes,according to some embodiments. As mentioned, interpolation is generallyless error-prone than extrapolation for determining any additionalmodulation levels not exhibited in the short-form demodulationreference. The versions of FIGS. 3A and 3B are also advantageous becausethey exhibited values that span the full range of amplitudes, andtherefore can mitigate both additive distortions and multiplicativedistortions, as discussed below.

If the version of FIG. 3A or 3B is adopted as the default standard, noadditional information about the modulation scheme needs to becommunicated. For example, it is unnecessary to indicate which referenceelement represents the minimum or maximum values, since the receiver caninterpolate between them in either case. In addition, with this version,the modulation order can be readily determined according to the phasedifference between the two phase values of the reference elements, thatis, 180, 90, 60, or 45 degree phase difference according to BPSK, QPSKor 16QAM, 64QAM, and 256QAM respectively. In addition, this version ofthe two-point short-form demodulation reference is unchanged, and theanalysis procedure is unchanged, regardless of whether the transmitteruses the carrier phase or not, since the calibration set phase valuesare derived from the exhibited values. In addition, the two-pointshort-form demodulation reference of FIG. 3A or 3B is configured tomitigate distortions due to noise and interference including bothadditive and multiplicative types, due to the use of interpolationbetween maximum and minimum levels in both amplitude and phase.Therefore, the calibration set values for amplitude and phase, whencalculated according to the methods disclosed herein, may include bothadditive and multiplicative distortions from noise and interference, andthose calibration set values may therefore compensate or mitigatemessage elements that are subjected to the same conditions as thedemodulation reference, including both the additive and multiplicativecomponents of noise and interference, according to some embodiments. Insummary, selecting the short-form demodulation reference of FIGS. 3A and3B as the default standard may provide a short but effective modulationlevel calibration, providing direct mitigation of noise andinterference, for both amplitude and phase distortions, and iscompatible with both high-performance and reduced-capability devices, inboth high-density traffic environments and sparse messagingenvironments.

FIG. 3C is a phase chart showing another exemplary embodiment of a shortlow-complexity demodulation reference such as a two-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the four amplitudes of 16QAM are shown ascircles 320, and two particular states are shown as points 321 and 322.The first point 321 exhibits the second-lowest phase and amplitudelevels, and the second point 322 has the highest amplitude and phaselevels. Thus the two points 321, 322 differ in amplitude by twoamplitude steps, and they differ in phase by two phase steps. First, thephase step can be determined by noting that the phase of point 322 isgreater than 270 degrees, and therefore the point 322 exhibits themaximum phase value. Accordingly, the estimated phase step may becalculated by subtracting the phase of point 322 from 360 degrees, thenmultiplying the difference by 2 to derive an estimated phase step, whichis closest to the standard phase step of 90 degrees in this case.Alternatively, if the receiver knows that the two points 321-322 differby two phase steps, the receiver may divide the difference in phase bytwo, and thereby derive the phase step without assuming anything aboutthe carrier phase. All of the phase levels can then be determined byrepeatedly adding that phase step to either one of the points 321-322,modulo 360, or by linearly interpolating between them. Counting thenumber of phases in this case, Nphase=4 which implies either QPSK or16QAM. The amplitude levels can be determined by noting that the twopoints 321-322 have different amplitudes, and therefore they are notQPSK modulated which has only one amplitude level. Therefore, themodulation scheme must be QAM, in which case Namp=Nphase, and asmentioned, Nphase=4 so the modulation scheme must be 16QAM. To calculatethe remaining amplitude levels of the modulation scheme from the pointsprovided, the receiver must know that one of them exhibits the maximumamplitude level, and that they are separated by twice the amplitudestep. This determination may be based on a convention or default or RRC(radio resource control) message or otherwise. Then the amplitude stepcan be calculated by subtracting the amplitude of the first point 321from the second point 322 and dividing by two (because they are twoamplitude steps apart). The remaining amplitude levels can then bedetermined by subtracting the amplitude step from the maximum amplitudelevel as exhibited by point 322, until all four amplitude levels aredetermined. In this way, all of the amplitude and phase modulationlevels of the modulation scheme can be determined if the receiver knowswhich format of short-form demodulation reference is used. Each messageelement can then be demodulated by comparing to the calibration set ofamplitude and phase levels so determined.

FIG. 3D is a modulation table showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a 2-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the modulation states of 16QAM are shown ascircles 330, and two of the modulation states are shown stippled as 331and 332. The first point 331 exhibits the amplitude and phase one stepabove the minimum. The second point 332 exhibits the maximum phase andmaximum amplitude levels. The two points 331-332 thus differ in phase bytwo phase steps, and they differ in amplitude by two amplitude steps.The modulation table shows the same set of points as the phase chart ofFIG. 3C.

FIG. 3E is a phase chart showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a two-point short-formdemodulation reference for a QPSK modulation, according to someembodiments. As depicted in this non-limiting example, the circle 340represents a particular amplitude, and the two indicated states 341, 342are modulation states with phase and amplitude as shown. For QPSK, thephase is varied between four values spaced apart by 90 degrees, and theamplitude is held constant. Thus the two points 341 and 342 are at thesame radius 340, indicating the same amplitude. The phase of the firstpoint 341 is the minimum phase plus one phase step and the second point342 is modulated at the minimum phase plus two phase steps. The receivercan determine that Namp=1 since both points 341-342 have the sameamplitude, and can determine that the modulation scheme is QPSK becausethe two points 331-332 are separated by 90 degrees in phase. Thereceiver can then calculate the remaining phase levels by repeatedlyadding that phase step to either of the points, modulo 360.

FIG. 3F is a modulation table showing an exemplary embodiment of a shortlow-complexity demodulation reference such as a two-point short-formdemodulation reference for QPSK, according to some embodiments. Asdepicted in this non-limiting example, the modulation table shows thefour states 350 of QPSK, with two of the states 351 and 352 stippled. Asdepicted in this non-limiting example, those two states 351, 352correspond to two phases which are one phase step apart, or 90 degreesapart, and at the same amplitude. Messages modulated in QPSK can bedemodulated using the two-point short-form demodulation reference bycalculating the phase step equal to the magnitude of the difference inphase between the two reference elements 351-352, and repeatedly addingor subtracting that phase step from/to one of the exhibited states351-352, thereby determining the four phase states. FIG. 3F shows thesame set of points as FIG. 3E. The receiver can calculate all of thestates of the modulation scheme from the short-form demodulationreference.

An advantage of the two-point short-form demodulation reference may bethat it is short, only two reference elements. Another advantage may bethat the two-point short-form demodulation reference may be added toanother message, even a short message, without undue consumption ofresources. Another advantage may be that the two-point short-formdemodulation reference may serve as a modulation calibration for variousorders of quadrature amplitude modulation or phase-shift keying, bycalculating the non-exhibited levels based on the amplitude values andphase values provided in the reference elements of the short-formdemodulation reference. Another advantage may be that distortions, inamplitude or phase or both, due to noise or interference, may beincluded in the amplitude and phase values of the reference elements,and therefore those distortions may be canceled when the receivedreference values are used to demodulate a subsequent message.

FIG. 4A is a sequence chart showing an exemplary embodiment of alow-complexity procedure for providing a two-point short-formdemodulation reference, according to some embodiments. The receivedsignal is shown on the first line, a processor on the second line, andresults are shown on the third line. As depicted in this non-limitingexample, the demodulation reference is a two-point short-formdemodulation reference 401, followed by a message 402 which is to bedemodulated. In this case, the message 402 is concatenated directly tothe reference 401, with no gap. The receiver first analyzes thereference elements of the two-point short-form demodulation reference401 and thereby determines amplitude and phase calibrations 403. In thiscase, the 2-point short-form demodulation reference exhibits the maximumand minimum amplitude modulation levels, the minimum phase modulationlevel, and the next higher phase level (separated by the phase step).The processor may then linearly interpolate between the maximum andminimum amplitude levels to determine intermediate amplitude levels,such as the four amplitude levels of 16QAM, and may include thosecalculated states in the calibration set 403, and may thereby determinethe amplitude levels by which the message elements are modulated. Theprocessor may also extrapolate the phase levels by calculating thedifference between the two phases provided, and then adding integermultiples of that difference to the phases provided (modulo 360degrees), and may thereby determine the phase levels by which themessage elements are modulated. Thus the processor can determine theamplitude and phase (A&P) levels of the modulation scheme.

Then, the processor analyzes each element of the message 402, comparingthe amplitude of the message element 402 to the calibration set 403, andthereby assigns an amplitude modulation level 404 to each of the messageelements. The processor then compares the phase of each message element402 to the calibration set 403, and thereby assigns a phase modulation(A&P) level 404 to each of the message elements. In addition, eachamplitude and phase modulation level in the calibration set may beassigned a binary code or other numerical representation, and themessage 402 may thereby be rendered as an output binary image 405. Inthis case, the message 402 is represented by a series of binary bits 405by concatenating the amplitude code A and the phase code P for eachmessage element.

FIG. 4B is a flowchart showing an exemplary embodiment of alow-complexity procedure for using a demodulation reference, accordingto some embodiments. As depicted in this non-limiting example, the2-point short-form demodulation reference again exhibits the maximum andminimum amplitude levels, and the minimum phase, and the next-higherphase level. A receiver compares message elements of a message toreference elements of a two-point short-form demodulation reference, andthereby determines the amplitude and phase modulation levels for each ofthe message elements.

At 450, a receiving entity receives a two-point short-form demodulationreference and, at 451, measures the maximum and minimum amplitude valuesas provided in its two reference elements, and also measures the phasevalues of each of its two reference elements representing a minimumphase and a next-higher phase level. At 453, a processor calculates theremaining amplitude levels by interpolation between the maximum andminimum amplitude levels provided. At 454, the processor calculates theremaining phase levels by extrapolation, by repeatedly adding the phasestep (equal to the phase difference between the first two points) to thesecond provided point, up to 360 degrees. At 455, the calibration set,including all of the modulation levels used in a modulation scheme, hasbeen determined, and a numerical code “A” has been assigned for eachamplitude level and a numerical code “P” has been assigned for eachphase level. At 456 (if not sooner), the message is received. At 457,each message element is compared to the amplitude and phase modulationcalibration levels, thereby determining the amplitude and phase level bywhich each message element was initially modulated. At 458, a binaryrepresentation of the message is prepared by concatenating the amplitudeand phase codes of the various message elements, and the procedure isdone at 459.

An advantage of providing a two-point short-form demodulation referencemay be that it is short, just two reference elements. Another advantagemay be that the maximum and minimum amplitude modulation states (or themaximum amplitude level and the adjacent amplitude level, or the minimumamplitude level and the adjacent amplitude level, among othercombinations) can be explicitly provided, and likewise the two lowestphase modulation states (or the minimum and maximum phases, or themaximum and the phase step, among other combinations) can be explicitlyprovided in the short-form demodulation reference, according to someembodiments. The receiver can then determine all the amplitude and phasemodulation states of the modulation scheme using the principles andmethods disclosed. Another advantage may be that distortions, inamplitude or phase or both, due to noise or interference, may beincluded in the amplitude and phase values of the reference elements,and therefore those distortions may be canceled when the receivedreference values are used to demodulate a subsequent message.

The systems and methods further include a one-point short-formdemodulation reference, with a length of just one reference element, asin the following examples.

FIG. 5A is a phase chart showing an exemplary embodiment of a very shortlow-complexity demodulation reference such as a one-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the circles 500 represent amplitudemodulation levels, and the indicated state 501 is a modulation state atthe maximum amplitude and at the maximum phase of the modulation scheme.Also shown is the width 505 of the amplitude modulation levels 500,extending from the minimum amplitude to the maximum amplitude. For thecase shown, the minimum amplitude is 0.5 times the maximum. Theamplitude ratio is the ratio of the minimum amplitude level divided bythe maximum amplitude level of the modulation scheme, in this case,which is 0.5. The one-point short-form demodulation reference may beused to demodulate elements of messages modulated in quadratureamplitude modulation or phase-shift keying, if the amplitude ratio isknown. The number of amplitude and phase levels can be determined fromthe phase of the single point 501 if the receiver knows Nphase. Thephase step is 360 divided by Nphase, and the remaining phase levels canbe found by repeatedly adding the phase step to the exhibited phase,modulo 360.

If, however, the receiver knows the carrier phase but does not knowNphase, then the receiver can calculate a phase step estimate equal totwice the difference between the exhibited phase and the carrier phase,then select the closest standard phase step value, and then repeatedlyadd that selected phase step to the exhibited phase to obtain all of thephase levels of the modulation scheme. Since the phases are modulo 360,that formula works regardless of whether the exhibited phase is theminimum, maximum, or an intermediate phase, so long as the maximum andminimum phase levels of the modulation scheme are spaced equally fromthe carrier phase. Due to noise or interference, the phase stepcalculated from the exhibited phase value may not exactly equal thestandard values of 180, 90, 60, and 45 degrees for BPSK, QPSK or 16QAM,64QAM, and 256QAM respectively. In that case, the receiver can selectthe closest of the standard values as the phase step, then add thatstandard phase step repeatedly to the measured phase value of thereference element to determine the other phase values. On the otherhand, if the receiver knows the number of phases Nphase, then thereceiver can calculate the phase step as 360/Nphase, and then add thatphase step repeatedly to the reference element phase value. In eithercase, the phase values in the calibration set may correspond to thephase values in a subsequent message, since they both include thecurrent noise and interference levels. Hence the calibration set,derived from the one-point short-form demodulation reference, maythereby mitigate that noise and interference in demodulating the messageelements.

The amplitude levels can be found in a similar way, given the amplituderatio. If the amplitude ratio is 1.0, there is no amplitude modulationand Namp=1, in which case the modulation scheme is BPSK or QPSKaccording to the number of phase levels as determined above. If theamplitude ratio is less than 1, the modulation scheme is QAM, and thenumber of amplitude levels equals the number of phase levels. Thoseamplitude levels can be found by calculating a second amplitude valueaccording to the exhibited amplitude value and the amplitude ratio. Ifthe exhibited amplitude value is the maximum amplitude level, then thesecond amplitude equals the exhibited amplitude value times theamplitude ratio. If the exhibited amplitude value is the minimumamplitude level, then the second point amplitude is the exhibitedamplitude value divided by the amplitude ratio. In this example, thereceiver is expected to know, by convention or default or messaging orotherwise, whether the single point exhibits the minimum or maximumamplitude level of the modulation scheme.

In some embodiments, additional information may be multiplexed in theprovided amplitude ratio, to assist the receiver in processing theone-point short-form demodulation reference. For example, the amplituderatio may be configured to be the maximum amplitude level divided by theminimum amplitude level if the exhibited amplitude level is the minimum,and the inverse of that if the exhibited level is the maximum.Alternatively, the sign of the amplitude ratio may be set by whether theexhibited amplitude value is the maximum or minimum. In either case, thereceiver may determine the opposite extremum (that is, the minimum levelif the maximum is exhibited, or the maximum if the minimum isexhibited), and thereby interpolate the remaining levels of themodulation scheme.

Having determined the maximum and minimum amplitude levels, the receivercan calculate the remaining amplitude levels by interpolating betweenthe exhibited amplitude value and the second amplitude value,representing the maximum and minimum amplitude levels of the modulationscheme. Therefore, a single modulated point is sufficient to determineall of the modulation states of a modulation scheme including PSK andQAM type modulation schemes. Since the reference element amplitude valueincludes the effects of noise and interference, the calibration setvalues obtained by this method may be used to demodulate the messageelement amplitude values with the same noise and interferencedistortions, and thereby at least partially mitigate those distortions.

FIG. 5B is a modulation table showing an exemplary embodiment of a veryshort low-complexity demodulation reference such as a one-pointshort-form demodulation reference, according to some embodiments. Asdepicted in this non-limiting example, the table shows the sixteenstates 510 of 16QAM, with one state 511 stippled, corresponding to thestate 501 shown in the previous figure. The state 511 corresponds to amaximum-amplitude, maximum-phase modulation state. Thus the two chartsof FIGS. 5A and 5B show the same information but in different forms.Messages modulated in 16QAM, or other orders of quadrature amplitudemodulation, as well as BPSK and QPSK, can be demodulated using thedepicted modulation table, as long as the amplitude ratio is known, andthe receiver knows whether the exhibited amplitude represents theminimum or maximum level. First, the phase levels can be found bydetermining the phase step from the phase level shown (by doubling theseparation between the exhibited phase and 360 degrees, in the exampleshown) or by convention or by dividing 360 by Nphase, then subtractingthe phase step repeatedly from the maximum phase level, modulo 360. Theextrapolation also determines Nphase according to the number of phasesteps that fit in 360 degrees. The amplitude levels can be found byinterpolation between the maximum and minimum amplitude, using theexhibited amplitude as one limit of interpolation and a second amplitudeas the other limit of interpolation, wherein the second amplitude equalsthe exhibited amplitude value divided by the amplitude ratio if theexhibited amplitude is the minimum, or the second amplitude equals theexhibited amplitude times the amplitude ratio if the exhibited amplitudeis the maximum.

In another embodiment, a modified amplitude ratio may be provided,configured to accommodate cases wherein the receiver does not knowwhether the exhibited amplitude is the maximum or minimum level. Themodified amplitude ratio depends on whether the exhibited amplitudevalue is the minimum or maximum level of the modulation scheme. Hence,the modified amplitude ratio accommodates both possibilities. If theexhibited amplitude is the minimum, then the modified amplitude ratio isthe maximum divided by the minimum amplitude levels of the modulationscheme. If the exhibited amplitude is the maximum, then the modifiedamplitude ratio is the minimum divided by the maximum. The receiver canthen calculate a second amplitude value by multiplying the exhibitedamplitude value by the modified amplitude ratio, and can interpolatebetween that second amplitude value and the exhibited amplitude value todetermine the intermediate amplitude levels, without knowing whether theexhibited amplitude is the maximum or the minimum. The modifiedamplitude ratio, being greater or less than 1 according to whether theminimum or maximum amplitude is exhibited, thereby determines themaximum and minimum interpolation limits, regardless of whether theexhibited amplitude is the minimum or maximum level.

FIG. 5C is a phase chart showing another exemplary embodiment of a veryshort low-complexity demodulation reference such as a one-pointshort-form demodulation reference, according to some embodiments. Theone-point demodulation reference may be used to calibrate the amplitudeand phase levels by which the message elements of messages aremodulated. As depicted in this non-limiting example, the circles 520represent amplitude modulation levels. Unlike the previous example, theindicated state 521 is modulated at the minimum amplitude and at theminimum phase. Also shown is the width of the amplitude levels as 525,extending from the minimum amplitude to the maximum amplitude. For thecase shown, the amplitude ratio (minimum/maximum) is 0.5; hence themaximum amplitude level is the exhibited level divided by the amplituderatio. The remaining amplitude and phase levels may be calculated byinterpolation (for amplitudes) and extrapolation (for phases) asdescribed above. The number of amplitude and phase levels can bedetermined from the phase of the single point 521, since the phase stepis generally twice the initial phase value (if the minimum phase), ortwice the difference between 360 and the exhibited phase (if the maximumphase), provided that the phases avoid the zero-degree carrier phase fornoise immunity. That phase step can be added to the initial point 521repeatedly to calculate the remaining points (but not greater than 360degrees). This determines the number of phase levels in the modulationscheme. If the modulation scheme is QAM, then the number of amplitudelevels is the same as the number of phase levels, and those amplitudelevels can be found by interpolating between the minimum level (which isexhibited in the one-point short-form demodulation reference in thiscase) and the maximum amplitude level (calculated by dividing theminimum by the amplitude ratio). If, however, the amplitude ratio is1.0, amplitude modulation is not used, and the modulation scheme iseither BPSK or QPSK, depending on the value of the first point's phase.Specifically, if the exhibited phase is 45 degrees or 315 degrees, themodulation scheme is QPSK, and if the exhibited phase is 90 or 270degrees, it is BPSK). In another embodiment, the receiver does not knowthe subcarrier phase and cannot determine a value for the phase of thesingle point, Nevertheless, if the receiver knows the modulation scheme(in this case 16QAM), the receiver can readily calculate the phase step(90 degrees in the depicted case) and repeatedly add that phase step tothe exhibited phase point, thereby determining all of the phase levelsof the modulation scheme, without knowledge of the carrier phase orwhether the exhibited phase is maximum or minimum or an intermediatelevel. It is sufficient for the receiver to know Nphase to fill in allthe other phase levels of the modulation scheme. In either case, then,the complete set of amplitude and phase modulation levels for themodulation scheme can be determined from the single short-formdemodulation point and the amplitude ratio if either the modulation typeor Nphase is known to the receiver.

FIG. 5D is a modulation table showing an exemplary embodiment of a veryshort low-complexity demodulation reference such as a one-pointshort-form demodulation reference, according to some embodiments. Asdepicted in this non-limiting example, the table shows the sixteenstates 530 of 16QAM, with one state 531 stippled, corresponding to thestate 521 shown in the previous figure. The state 531 corresponds to aminimum-amplitude, minimum-phase modulation state. Thus the two chartsof FIGS. 5C and 5D show the same information but in different forms.Messages modulated in 16QAM, or other order of quadrature amplitudemodulation, as well as BPSK and QPSK, can be demodulated using thedepicted modulation table, as long as the receiver knows the amplituderatio, whether the exhibited amplitude value is the minimum or maximumamplitude level, and the number of phase levels of the modulationscheme. For a scheme not employing amplitude modulation, such as BPSKand QPSK, the amplitude ratio is 1.0. The phase levels can be calculatedby extrapolation in phase from the phase exhibited if the carrier phaseis known, or from 360/Nphase if Nphase is known. The amplitude levelscan be calculated by interpolation between the maximum and minimumamplitude, using the exhibited amplitude and the known amplitude ratio.

FIG. 5E is a phase chart showing an exemplary embodiment of a very shortlow-complexity demodulation reference such as a one-point short-formdemodulation reference for QPSK, according to some embodiments. Asdepicted in this non-limiting example, the circle 540 represents theconstant amplitude of the modulation scheme. The indicated state 541 ismodulated at the single amplitude and at the minimum phase of themodulation scheme. The width of the amplitude levels is zero in thiscase, so the minimum amplitude equals the maximum amplitude as shown,and the amplitude ratio is 1.0. The one-point short-form demodulationreference may be used to calibrate elements of messages modulated inQPSK, after calculating the remaining phase levels by phaseextrapolation, as discussed previously.

FIG. 5F is a modulation table showing an exemplary embodiment of alow-complexity demodulation reference such as a one-point short-formdemodulation reference, according to some embodiments. As depicted inthis non-limiting example, the table shows the four states 550 of QPSK,with one state 551 stippled, corresponding to the state 541 shown in theprevious figure. The state 551 corresponds to a minimum-phase modulationstate, and with constant amplitude. Thus the two charts of FIGS. 5E and5F show the same information but in different forms.

An advantage of the one-point short-form demodulation reference may bethat it is very small, just one reference element, and thus can be addedto messages with only a very slight increase in resource usage. Anotheradvantage may be that it may be easy for receiver processors to use theshort-form demodulation reference to demodulate messages, since theamplitudes of the message elements are all between the minimum andmaximum amplitude levels as calculated according to the amplitude ratio,and the phase of the message element is between the maximum and minimumphase levels as calculated according to the number of phase levels.Another advantage may be that distortions, in amplitude or phase orboth, due to noise or interference, may be included in the amplitude andphase values of the reference elements, and therefore those distortionsmay be substantially canceled when the received reference values areused to demodulate a subsequent message.

FIG. 6A is a sequence chart showing an exemplary embodiment of alow-complexity procedure for providing and using a one-point short-formdemodulation reference, according to some embodiments. A received signalis shown on the first line, a processor on the second line, and a resultis shown on the third line. As depicted in this non-limiting example, anamplitude ratio 600, equal to the minimum amplitude level in themodulation scheme divided by the maximum, is initially received as anRRC message, for example. A demodulation reference 601 is laterreceived, in this case a one-point short-form demodulation reference601, followed later by a message 602 which is to be demodulated. Theshort-form demodulation reference 601 is not time-synchronized with themessage 602 in this case, other than to precede the message 602. In someembodiments, the ratio message 600 may also indicate whether theshort-form demodulation reference 601 exhibits the minimum or maximumamplitude level of the modulation scheme. In other embodiments, thatamplitude information may be established by a system informationmessage, or by convention, or otherwise. In some embodiments, theamplitude ratio is configured to indicate whether the minimum or maximumamplitude is exhibited, such as by making the amplitude ratio negativeif the minimum amplitude is exhibited and positive if the maximumamplitude is exhibited, for example. In each case, the processor candetermine how to use the amplitude ratio 600 to calculate the other,non-exhibited, amplitude levels.

The processor then analyzes the sole reference element of the one-pointshort-form demodulation reference 601 using the provided amplitude ratio600, and thereby determines the amplitude and phase calibration set 603,which includes the values of the amplitude levels and the phase valuesof the modulation scheme. In this example, the 1-point short-formdemodulation reference includes the maximum amplitude level and theminimum phase level. The processor may determine the phase modulationlevels by, for example, calculating a phase step size equal to twice theminimum phase provided, and dividing 360 degrees by that phase step.Alternatively, if the modulation scheme is already known, or if thenumber of phase levels is already known, the processor may calculate thephase step size equal to 360 degrees divided by the number of phaselevels. The processor may then add integer multiples of that step sizeto the minimum phase provided (modulo 360 degrees), and may therebydetermine the phase levels by which the message elements are modulated.As a third option, the processor may multiply the minimum phase by oddintegers to determine the remaining phase levels, up to 360 degrees.

In addition, the processor may calculate the amplitude levels based onthe reference element and the amplitude ratio. If the short-formdemodulation reference 601 exhibits the maximum amplitude level, theprocessor may calculate a minimum amplitude level by multiplying themaximum amplitude level by the amplitude ratio, and may then interpolatebetween the maximum and minimum amplitude levels to determineintermediate levels. If the short-form demodulation reference 601exhibits the minimum amplitude level, the processor may calculate amaximum amplitude level by dividing the minimum amplitude level by theamplitude ratio. If the amplitude ratio is 1, there is only oneamplitude level and the modulation scheme is not amplitude modulated. Ifthe amplitude ratio is not 1, the number of amplitude levels equals thenumber of phase levels. The amplitude and phase levels, thus calculatedfrom the reference amplitude value and the reference phase value, plusattendant calculations as described, form the amplitude and phase (A&P)calibration set 603.

Then, the processor analyzes each resource element of the message 602,comparing each message amplitude value and each message phase value tothe amplitude levels and phase levels in the calibration set 603, andthereby assigns an amplitude modulation level and a phase modulationlevel 604 to each of the message elements 602. Then each amplitude andphase modulation level may be assigned a binary code, or other numericalcode, and the entire message 602 can then be represented by a series ofbinary bits 605 by concatenating, or otherwise combining, the codes foreach message element. (If the amplitude ratio is 1, the amplitudecomparison step may be omitted, and the binary codes representingamplitude may be omitted, since only phase modulation is then relevant.)

FIG. 6B is a flowchart showing an exemplary embodiment of alow-complexity procedure for using a demodulation reference, accordingto some embodiments. As depicted in this non-limiting example, areceiver compares elements of a message to calibrations based on aone-point short-form demodulation reference, and thereby determines themodulation levels, in amplitude and phase, for each of the messageelements.

At 650, the receiving entity either obtains or already knows theamplitude ratio, which is the ratio of the minimum to maximum amplitudelevels of the modulation scheme that the message is modulated in. Theamplitude ratio may be a standard convention and built-in for example,or it may be provided from an information source such as a networkdatabase, or provided as part of a system information message or a RRCmessage, or multiplexed in the amplitude ratio value, or otherwiseavailable to the receiving entity. At 651, the receiving entity receivesa one-point short-form demodulation reference (such as that of FIG. 5A)and, at 652, measures the maximum amplitude value and, in this case, themaximum phase value, as exhibited in the short-form demodulationreference. At 653, the entity calculates a minimum amplitude modulationlevel by multiplying the maximum amplitude times the amplitude ratio. At654, the entity calculates a phase step size equal to twice thedifference between 360 degrees and the maximum phase value, and a numberof phase levels equal to 360 degrees divided by the phase step size. (Inanother embodiment, the network may indicate the number of phase levelsNphase in the RRC message or the system information message along withthe amplitude ratio, in which case the receiver can determine the phasestep and the other phase levels without assuming that the exhibitedphase has a particular relationship with the carrier phase.) The entityalso calculates a number of amplitude levels. If the amplitude ratio is1, then there is only one amplitude level and the modulation scheme isBPSK or QPSK. If the amplitude ratio is different from 1, then themodulation scheme is some order of QAM and the number of amplitudelevels is equal to the number of phase levels.

At 655 the entity calculates the amplitude levels and phase levels notexplicitly provided, using interpolation and extrapolation as describedabove, thereby completing the calibration set. In this case, the entityrepeatedly subtracts the phase step from the exhibited reference phasevalue, modulo 360, and thereby determines all of the phase levels in thecalibration set. At 656, the entity receives the message to bedemodulated. At 657, the entity compares each element of the message tothe amplitude and phase levels in the calibration set. At 658, eachmessage amplitude value of each element of the message is then 658assigned a specific modulation state by matching the message amplitudevalue with one of the calibrated amplitude levels, and each messagephase value of each element of the message is assigned a specificmodulation state by matching the message phase value with one of thecalibrated phase levels. At 659, a binary representation of the messageis prepared by concatenating the amplitude and phase codes of thevarious message elements, and is done at 660.

In some cases, the receiver may already know the number of amplitude andphase levels. For example, if a particular modulation scheme has alreadybeen agreed upon, the receiving entity only needs the amplitude andphase values in the one-point short-form demodulation reference, and theamplitude ratio, to calibrate all of the amplitude and phase levels inthe calibration set. Thus if the number of phase levels in themodulation scheme is already known, the processor can calculate thephase step size equal to 360 degrees divided by the number of phaselevels, and can then calculate the additional phase levels by adding thephase step size to the exhibited phase, modulo 360. If the number ofamplitude levels in the modulation scheme is already known, theprocessor can determine a second amplitude by multiplying the amplituderatio by the exhibited amplitude value, and then can calculate theintermediate amplitude levels by interpolation.

An advantage of providing a one-point short-form demodulation referencemay be that it is very short, just one reference element. Anotheradvantage may be that the maximum or minimum amplitude modulation andthe maximum or minimum phase modulation values can be explicitlyprovided in the short-form demodulation reference. Another advantage maybe that additional amplitude and phase levels may be calculated from thevalues explicitly exhibited, if the amplitude ratio is provided oralready known to the receiver. Another advantage may be thatdistortions, in amplitude or phase or both, due to noise orinterference, may be included in the amplitude and phase values of thereference elements, and therefore those distortions may be substantiallycanceled when the received reference values are used to demodulate asubsequent message.

FIG. 7A is a schematic showing an exemplary embodiment of a wavemodulated using pulse-amplitude modulation, according to someembodiments. As depicted in this non-limiting example, wavesrepresenting modulated signals are shown as in an oscilloscope display,with voltage vertical and time horizontal. The intent is to illustratePAM (pulse-amplitude modulation) and show how it can be demodulatedusing the systems and methods disclosed herein. In PAM, a messageelement may be modulated by adding two sinusoidal signals, a firstsignal with a first amplitude and a first phase of zero degrees, plus asecond signal with a second amplitude and a second phase of 90 degrees.The zero-degree signal is called a “real” component, and the 90-degreesignal is the “imaginary” component. The first and second amplitudes arethen separately modulated and combined before transmission. For example,16QAM may be represented as a summed signal in which the first amplitudeis one of four predetermined levels, and the second amplitude isseparately configured to one of the four levels, thereby providing 16valid modulation states when combined. Negative amplitudes areequivalent to 180-degree phase reversals. The receiver can thendemodulate the signal by measuring the real and imaginary componentsseparately.

In the figure, a first wave 701 is phased at zero degrees (that is, itsmaximum value falls at zero degrees, as in a cosine curve) and has aparticular amplitude as shown. The second wave 702 is phased at 90degrees, and has another amplitude (in this case negative) at the90-degree phase. The third wave 703 is a summed wave formed by addingthe first and second waves 701-702, and thus is the PAM waveform thatwould be transmitted using the first and second waves 701, 702 as thereal and imaginary components. A receiver, upon detecting the third wave703, can demodulate it by measuring the zero-degree “real” amplitude,indicated as a square 704 at zero degrees where the imaginary wavepasses through zero, and by measuring the 90-degree “imaginary”amplitude 705 where the real wave crosses zero. The receiver can therebydetermine the modulation state of the message element by comparing thoseamplitudes to a modulation constellation.

FIG. 7B is a constellation table showing an exemplary embodiment of ademodulation scheme based on real and imaginary components, according tosome embodiments. As depicted in this non-limiting example, modulationstates 710 are depicted as squares with a real amplitude shown in thehorizontal direction and the imaginary amplitude vertically. In thiscase, the modulation scheme is 16QAM, and the real and imaginaryamplitudes may have positive and negative values. One of the modulationstates is stippled 711, representing a maximum real amplitude and aminimum imaginary amplitude. Hence, the state 711 corresponds to thewave 703.

The systems and methods disclosed herein are readily applicable toPAM-modulated messages, with real and imaginary substituting foramplitude and phase, according to some embodiments. Other technologiesfor modulation and demodulation of wireless signals may likewise beemployed with the short-form demodulation references and the processingmethods disclosed herein, with straightforward adaptation such assubstituting amplitude-phase states for real-imaginary states, forexample. Thus, a wide range of modulation technologies may bedemodulated using the disclosed systems and methods, according to someembodiments.

FIG. 8A is a sketch showing an exemplary embodiment of a resource grid800 according to some embodiments. One slot is indicated as 801 and oneresource block as 802. Symbol times are marked at 804 and subcarriers as805. A single resource element is shown as 807. The first symbol time isoutlined. As depicted in this non-limiting example, a message 809, shownin stipple, is frequency-spanning in the fifth symbol period.Demodulation references 808, shown in grid hatch, are two-pointshort-form demodulation references in this case. Each two-pointshort-form demodulation reference 808 occupies just two resourceelements, inserted among the message elements. In this case, the firsttwo subcarriers in each resource block are used as demodulationreferences 808 throughout the message 809. Each two-point short-formdemodulation reference 808 includes sufficient amplitude and phaseinformation to update all of the amplitude and phase levels of thecalibration set in the presence of current interference, and therebyimproves the interference mitigation of the message 809. Importantly,the average distance (in frequency) from each message element to theclosest demodulation reference is only 3 subcarriers, yet the additionalresource usage is less than 17%. The figure thus demonstrates thatinserting a two-point short-form demodulation reference 808 in eachresource block of a frequency-spanning message 809 providestime-frequency recalibrations of modulation levels, and localizedrecalibrations for improved interference mitigation, yet causes only asmall increase in resource and energy usage, according to someembodiments.

FIG. 8B is a sketch showing an exemplary embodiment of a resource grid850 according to some embodiments. As depicted in this non-limitingexample, the resource grid 850 includes three slots and one resourceblock. Two time-spanning messages are shown in subcarriers 1 and 9. Eachmessage is interspersed with one-point short-form demodulationreferences. A first message 859 includes a one-point short-formdemodulation reference 858 in the first symbol period of each slot. Theone-point short-form demodulation references 858 thereby providesufficient modulation information to refresh the calibration set on thetime scale of one slot, at a cost of only about 7% of the messageresource elements.

The figure also shows a second message 869 in the ninth subcarrier. Thesecond message 869 is interspersed by one-point short-form demodulationreferences 868 in every seventh symbol time, thereby providinginterference mitigation on a time scale corresponding to a half-slot,for a resource usage increase of about 14%. The average distance from amessage element to the nearest reference element is reduced to 2 symbolperiods in the depicted example. Such close proximity between message869 and references 868 provides further improved interferencemitigation.

The updated demodulation information provided in the one-pointshort-form demodulation references 808 or 858 or 868 may be employed invarious ways. In one embodiment, the receiver may be configured todemodulate each portion of the message 809 or 859 or 869 according tothe updated modulation levels provided by the immediately precedingshort-form demodulation reference 808 or 858 or 868. In that case, eachportion of the message 809 or 859 or 869 is demodulated according to theimmediately preceding short-form demodulation reference 808 or 858 or868.

In a second embodiment, the receiver may be configured to demodulateeach portion of the message 809 or 859 or 869 by averaging the twoshort-form demodulation references 808 or 858 or 868 adjacent to thatmessage portion, that is, by averaging the corresponding modulationlevels in the short-form demodulation references 808 or 858 or 868immediately preceding and immediately following each message portion 809or 859 or 869. For example, the receiver may average each correspondingamplitude level in the preceding and following short-form demodulationreferences 808 or 858 or 868, and also average each corresponding phaselevel of the two short-form demodulation references 808 or 858 or 868,and then may demodulate the intervening message portion according tothose average amplitude and phase levels. By accounting for interferenceat both ends of each message portion, the receiver may mitigate variableinterference more accurately than using just the preceding short-formdemodulation reference to demodulate the message portion.

In a third embodiment, the receiver may be configured to calculate aweighted average for each amplitude and phase level in the modulationscheme. The weighted average may be obtained by weighting theimmediately preceding and immediately following short-form demodulationreferences. The weighting may be according to the distance, in time orfrequency, between each message element and the two proximate short-formdemodulation references. For example, the calibration set for eachmessage element may be calculated by interpolating between the precedingand following demodulation references. For example, the receiver maydemodulate a particular message element that is in the middle of themessage portion (and hence equidistant from the preceding and followingshort-form demodulation references) by weighting the preceding andfollowing values equally. For the first message element in the messageportion, on the other hand, the preceding short-form demodulationreference may be weighted heavily (since it is closer) and the followingshort-form demodulation reference may be weighted only lightly.Likewise, for the last message element in a message portion, thereceiver may heavily weight the following short-form demodulationreference and lightly weight the preceding one. In this way, thereceiver may interpolate between the preceding and followingdemodulation reference, and thereby calculate a distance-weightedcalibration set associated with each message element according to itsdistance from the preceding and following demodulation references, andthen may demodulate each element of the message using that weightedaverage. The resulting demodulation may thereby mitigate variableinterference more effectively than a non-weighted average.

In a fourth embodiment, the receiver may be configured to average aplurality of the preceding short-form demodulation references, andoptionally one or more of the following short-form demodulationreferences as well, in order to obtain a more accurate determination ofthe levels of the modulation scheme. Averaging multiple demodulationreferences may provide a more precise determination of the correctdemodulation levels when there is random noise in the receiver, such aselectronic noise, which is then amplified in the amplifier of thereceiver. In some cases, noise may be relatively stable or slowlychanging in time or frequency, in which case the averaging of several ofthe short-form demodulation references may provide a more precisedetermination of the levels.

Interference, on the other hand, is generally highly structured infrequency and time because it is likely due to competing messages fromadjacent cells, or from electrical machinery or the like. Averagingmultiple short-form demodulation references may be counter-productivewhen interference is larger than noise, because the interferencegenerally changes rapidly, such as changing between successive instancesof the demodulation reference. If the interference changes significantlyover a time equal to the averaging time of the short-form demodulationreferences, then the message elements that immediately follow thosechanges in the interference are likely to be incorrectly demodulated.Therefore, when interference is greater than noise, the weighted-averageembodiment described above, involving a weighted average between twoshort-form demodulation references that precede and follow the messagesection, may provide better mitigation and fewer message faults, thanaveraging multiple preceding and multiple following short-formdemodulation references. In contrast, when noise is greater thaninterference (and is sufficiently stable in time or frequency), then inthat case the averaging of multiple short-form demodulation referencesmay provide a more accurate set of level values than a single short-formdemodulation reference.

In some embodiments, a formula may be provided to assist user devicesand base stations in deciding which type of averaging is expected toresult in fewest message faults, according to the current conditions.Conditions that may affect the choice may include factors such as thetraffic density, the prior fault rate, the average noise amplitude, themaximum range of interference fluctuations, and the like. The formulamay be based on machine learning and/or artificial intelligence. Theformula may be configured to provide, as output, the most suitable typeof averaging or interpolating of short-form demodulation referencevalues, according to the current network and background and messagingconditions. For example, if noise dominates, the formula may recommendaveraging multiple short-form demodulation references to obtain a moreaccurate value of each modulation level, whereas if interferencedominates, the formula may recommend not averaging at all, or else usingthe weighted averaging based on distance from the preceding andfollowing short-form demodulation references. In this way, the formulamay assist the receiver in mitigating both electronic noise andfluctuating interference while minimizing message faults under bothconditions.

In some embodiments, a short-form demodulation reference may indicatethe beginning and/or ending of a message. User devices often havedifficulty identifying downlink control messages due to the large numberof possible positions and sizes of the messages. User devices areexpected to test all of the possible combinations of starting locationand length of possible downlink control messages by unscrambling eachcandidate message and comparing to an included CRC, for example. Theshort-form demodulation reference can greatly simplify this process byindicating, with a characteristic pattern of reference elements, thebeginning and/or ending of a message. For example, a two-pointshort-form demodulation reference having the maximum amplitude and phasein its first reference element and the minimum amplitude and phase inits second reference element, can be placed at the start of the message,to indicate where the message begins. The end of the message may beindicated by another, optionally different, pattern of short-formdemodulation reference, such as the minimum amplitude and phase followedby the maximum amplitude and phase. The receiver may be configured tosearch for the beginning and ending patterns among the receivedelements, and thereby identify messages, or at least greatly reduce thenumber of candidate messages that the receiver needs to test. Inaddition, the two-point short-form demodulation references at thebeginning and ending of the message may assist in demodulating themessage.

An advantage of providing multiple short-form demodulation references,such as one-point or two-point short-form demodulation references,interspersed among portions of a message, may be that the modulationlevels of the message elements may be recalibrated frequently thereby,resulting in interference mitigation on short time and frequency scales.In a dense radio environment, with large numbers of devices transmittingon various frequencies at various times, message faults may be reducedby providing demodulation recalibrations in close proximity to themessage elements they are intended to demodulate. Use of a shortdemodulation format, such as a short-form demodulation referenceoccupying just one or two resource elements, may minimize the additionalenergy consumed and electromagnetic background generated. Anotheradvantage may be that distortions, in amplitude or phase or both, due tonoise or interference, may be included in the amplitude and phase valuesof the reference elements, and therefore those distortions may becanceled in a subsequent message demodulated using those referencevalues.

Numerous versions of short-form demodulation references are disclosedherein, each with different properties, and many others are possibleusing the mathematical relationships discussed, or other equivalentmathematical relationships. Selecting which one to use in any messagingsituation is a complex problem. An algorithm may be developed to selectan appropriate or optimal type of short-form demodulation referencedepending on wireless conditions, the message, capabilities of thetransmitter and receiver, current traffic conditions, QoS requested, andmany other considerations. A 4-point short-form demodulation referenceprovides more information and redundancy than the 2-point version, whilethe 1-point version is very short but requires that the amplitude ratiobe predetermined. Other-point versions (3, 6, etc. points) are alsopossible. In some applications, keeping the message short may beparamount, whereas in other applications the additional redundancy andreliability of the 4-point version may be preferred. Some applicationsmay prioritize low latency, while others may require high reliability,and still others may need reduced complexity. Different versions may beoptimal for different modulation schemes, such as those with and withoutamplitude modulation. The transmitting processor may select the size andformat according to each message situation. Alternatively, a conventionmay be established favoring one of the short-form demodulation versionsas a default for all situations. As a further option, various versionsmay be recommended according to current parameters such as the energydensity and time-frequency properties of current interference.

As a further option, artificial intelligence (AI) or machine learningmay be used to prepare an algorithm, which is configured to select aparticular demodulation reference version according to the messagingsituation. To prepare such an algorithm, a large number of messagingevents may be tracked (or recorded or analyzed) by one or more basestations (or core networks or other networking entities). The data maybe analyzed by an AI structure such as a neural net, which takes ininput parameters and calculates output values according to a number ofinternal variables which are adjustable. For example, the inputparameters may include the current traffic density, number of activelycommunicating user devices, average size of messages, amount and type ofexternal interference, the size and type of short-form demodulationreference employed in various messaging situations, and the QoSrequirements related to each message, as well as a measure of theresulting network performance. The AI structure may also take as inputthe expected costs, such as resource element usage, delays, subsequentmessage failures, and the like. The AI structure may be configured togenerate outputs such as a prediction of the subsequent networkperformance, which may then be compared to the measured networkperformance, to judge how accurate the predictions are. Alternatively,the outputs may include a suggested format of a short-form demodulationreference according to current conditions, which users and base stationsmay then employ. The AI structure may also compare the costs andadvantages of the standard 5G/6G DMRS reference to the various formatsof short-form demodulation references, and may thereby address a greaterrange of use cases. The variables may then be varied to optimize, or atleast improve, the accuracy of the outputs or predictions.

An algorithm may be derived from the AI structure when the outputs haveachieved a sufficient accuracy. The algorithm may be the AI structureitself, or the AI structure condensed by freezing the variables andexcising any inputs and internal functions that have demonstrated littleeffect on the outputs, for example. Alternatively, an algorithm may beprepared to mimic the AI outputs according to the input values, butusing a different and preferably simpler calculation technique, such asan analytic function or a computer program or an interpolation table,among many other envisioned calculation options. The algorithm may thenbe provided to base stations and user devices so that they may makeoptimal, or at least improved, decisions regarding demodulationreferences according to the situation.

The algorithm may also provide assistance to the transmitter, indeciding which type of short-form demodulation reference to use, and howoften to include them in the message. For example, the algorithm maytake as input a measure of the interference levels observed at thetransmitter, other measures of interference measured by the receivingentity and communicated to the transmitter, a previously-determinedlevel of noise in the transmission process, a previously-determinedlevel of noise in the receiver and communicated to the transmitter, thespectrum of variations in noise or interference versus time or frequencyor both, among other possible considerations. The algorithm may furtherinclude receiver preferences, such as requiring high reliability ratherthan low latency, or vice versa. The length of the message, the numberof competing users, the expected traffic density and other networkparameters may also contribute to the algorithm's determination.

Due to the potentially large number of inputs and adjustable variablesin the model, and the very large amount of training data likely neededfor convergence of the model, the AI structure is preferably prepared ina supercomputer. The supercomputer may be a classicalsemiconductor-based computer, with sufficient speed and thread count andprocessor count to perform the model training in a feasible amount oftime. Alternatively, the supercomputer may be a quantum computer having“qbits” or quantum bits as its working elements. Quantum computers mayprovide special advantages to solving AI models because they can veryrapidly explore a complex terrain of values, such as the highlyinterrelated effects of the various inputs on the output results.Therefore, the systems and methods include a quantum computer programmedto include an AI structure and trained on network performance data andon input parameters including interference and noise parameters, messageparameters, and the like as discussed above.

As a further option, a wireless standards committee may select one ofthe short-form demodulation reference versions as a default standard.The selection may be based, at least in part, on the artificialintelligence or machine learning structure results or the algorithmderived from it.

For a handy universal default, the embodiment of FIG. 3A, a two-pointshort-form demodulation reference showing the maximum and minimum phaseand the maximum and minimum amplitude, is offered as an advantageouscandidate for such standardization, because the receiver can calculatethe remaining amplitude and phase levels of the modulation scheme usinginterpolation alone, with no extrapolation or logic involved, accordingto some embodiments. In addition, using the methods disclosed herein,the values of Nphase and Namp (if not already known to the receiver) canalso be calculated from the levels exhibited in the short-formdemodulation reference of FIG. 3A, thereby identifying the modulationscheme. All of the amplitude and phase levels of the modulation schemecan therefore be determined from the 2-point short-form demodulationreference using low-complexity logic and arithmetic, as described. Thedefault short-form demodulation reference can then be transmittedperiodically, or prepended to messages, or prepended and appended tomessages, or interspersed multiply within longer messages.

As another possible advantage, the 2-point short-form demodulationreference, or other default, when prepended to a message, may therebyindicate exactly where the message begins, and also whether the messageis frequency-spanning or time-spanning, thereby greatly simplifyingdetection of incoming messages. For example, the receiver can scan theactive bandwidth for the characteristic code of the short-formdemodulation reference, such as (1111 0000) representing the maximumamplitude and phase, followed by the minimum amplitude and phase, of thetwo reference elements as discussed above. The end of the message may beindicated by an ending configurations such as (0000 1111). By findingthose characteristic patterns, the receiver may determine the startingand ending points of the message. In 5G and 6G, it is generallydifficult for user devices to determine the starting point of a message,absent such a characteristic initial code. In addition, the orientationof the two reference elements, as time-spanning or frequency-spanning,thereby indicate whether the subsequent message is time-spanning orfrequency-spanning. For example, a sidelink message may be time-spanningor frequency-spanning according to the transmitting entity's preference.In addition, the short-form demodulation reference may be advantageouslyemployed on low-complexity or legacy channels as well ashigh-performance managed channels of 5G/6G, thereby providing compactand easy-to-use modulation calibration for each message. Moreover, thesmall size of the default short-form demodulation reference may be anenabling factor for agile interference mitigation in noisy environments,because the short short-form demodulation references may be placedliberally within messages at low cost, especially in regions withinterference problems.

The wireless embodiments of this disclosure may be aptly suited forcloud backup protection, according to some embodiments. Furthermore, thecloud backup can be provided cyber-security, such as blockchain, to lockor protect data, thereby preventing malevolent actors from makingchanges. The cyber-security may thereby avoid changes that, in someapplications, could result in hazards including lethal hazards, such asin applications related to traffic safety, electric grid management, lawenforcement, or national security.

In some embodiments, non-transitory computer-readable media may includeinstructions that, when executed by a computing environment, cause amethod to be performed, the method according to the principles disclosedherein. In some embodiments, the instructions (such as software orfirmware) may be upgradable or updatable, to provide additionalcapabilities and/or to fix errors and/or to remove securityvulnerabilities, among many other reasons for updating software. In someembodiments, the updates may be provided monthly, quarterly, annually,every 2 or 3 or 4 years, or upon other interval, or at the convenienceof the owner, for example. In some embodiments, the updates (especiallyupdates providing added capabilities) may be provided on a fee basis.The intent of the updates may be to cause the updated software toperform better than previously, and to thereby provide additional usersatisfaction.

The systems and methods may be fully implemented in any number ofcomputing devices. Typically, instructions are laid out on computerreadable media, generally non-transitory, and these instructions aresufficient to allow a processor in the computing device to implement themethod of the invention. The computer readable medium may be a harddrive or solid state storage having instructions that, when run, orsooner, are loaded into random access memory. Inputs to the application,e.g., from the plurality of users or from any one user, may be by anynumber of appropriate computer input devices. For example, users mayemploy vehicular controls, as well as a keyboard, mouse, touchscreen,joystick, trackpad, other pointing device, or any other such computerinput device to input data relevant to the calculations. Data may alsobe input by way of one or more sensors on the robot, an inserted memorychip, hard drive, flash drives, flash memory, optical media, magneticmedia, or any other type of file-storing medium. The outputs may bedelivered to a user by way of signals transmitted to robot steering andthrottle controls, a video graphics card or integrated graphics chipsetcoupled to a display that maybe seen by a user. Given this teaching, anynumber of other tangible outputs will also be understood to becontemplated by the invention. For example, outputs may be stored on amemory chip, hard drive, flash drives, flash memory, optical media,magnetic media, or any other type of output. It should also be notedthat the invention may be implemented on any number of different typesof computing devices, e.g., embedded systems and processors, personalcomputers, laptop computers, notebook computers, net book computers,handheld computers, personal digital assistants, mobile phones, smartphones, tablet computers, and also on devices specifically designed forthese purpose. In one implementation, a user of a smart phone orWi-Fi-connected device downloads a copy of the application to theirdevice from a server using a wireless Internet connection. Anappropriate authentication procedure and secure transaction process mayprovide for payment to be made to the seller. The application maydownload over the mobile connection, or over the Wi-Fi or other wirelessnetwork connection. The application may then be run by the user. Such anetworked system may provide a suitable computing environment for animplementation in which a plurality of users provide separate inputs tothe system and method.

It is to be understood that the foregoing description is not adefinition of the invention but is a description of one or morepreferred exemplary embodiments of the invention. The invention is notlimited to the particular embodiments(s) disclosed herein, but rather isdefined solely by the claims below. Furthermore, the statementscontained in the foregoing description relate to particular embodimentsand are not to be construed as limitations on the scope of the inventionor on the definition of terms used in the claims, except where a term orphrase is expressly defined above. Various other embodiments and variouschanges and modifications to the disclosed embodiment(s) will becomeapparent to those skilled in the art. For example, the specificcombination and order of steps is just one possibility, as the presentmethod may include a combination of steps that has fewer, greater, ordifferent steps than that shown here. All such other embodiments,changes, and modifications are intended to come within the scope of theappended claims.

As used in this specification and claims, the terms “for example”,“e.g.”, “for instance”, “such as”, and “like” and the terms“comprising”, “having”, “including”, and their other verb forms, whenused in conjunction with a listing of one or more components or otheritems, are each to be construed as open-ended, meaning that the listingis not to be considered as excluding other additional components oritems. Other terms are to be construed using their broadest reasonablemeaning unless they are used in a context that requires a differentinterpretation.

The invention claimed is:
 1. A method for demodulating a messagecomprising message elements, each message element modulated according toa modulation scheme comprising pulse-amplitude modulation (“PAM”),wherein the modulation scheme comprises integer Namp amplitude levels,each amplitude level comprising one of the predetermined amplitudes ofthe modulation scheme, the method comprising: receiving a demodulationreference comprising integer Nref reference elements, Nref less than orequal to four, each reference element modulated according to themodulation scheme; determining, for each reference element, a referenceI-branch signal and a reference Q-branch signal at 90 degrees phaserelative to the reference I-branch signal; determining the Nampamplitude levels of the modulation scheme according to the referenceI-branch signals and the reference Q-branch signals; receiving themessage; for each message element, determining a message I-branchamplitude value and determining which of the Namp amplitude levels mostclosely matches the message I-branch amplitude value, and determining amessage Q-branch amplitude value and determining which of the Nampamplitude levels most closely matches the message Q-branch amplitudevalue; whereby each amplitude “level” is one of the amplitudes within amodulation scheme as provided by the reference I-branch and referenceQ-branch signals or combinations thereof, and each amplitude “value” isan amplitude of a particular message element as measured by a receiver.2. The method of claim 1, wherein the demodulation reference and themessage are transmitted according to 5G or 6G technology.
 3. The methodof claim 1, wherein the determining the Namp amplitude levels comprises:for each reference element, determining a first amplitude level of themodulation scheme according to the reference I-branch signal, anddetermining a second amplitude level of the modulation scheme accordingto the reference Q-branch signal; and calculating one or more additionalamplitude levels of the modulation scheme by mathematically combiningtwo or more of the previously determined amplitude levels of themodulation scheme.
 4. The method of claim 3, wherein: the modulationscheme includes a largest positive amplitude level and a largestnegative amplitude level; at least one of the reference I-branch orQ-branch signals comprises the largest positive amplitude level, and atleast one of the reference I-branch or Q-branch signals comprises thelargest negative amplitude level.
 5. The method of claim 4, wherein: thecalculating one or more additional amplitude levels of the modulationscheme comprises interpolating between the largest positive amplitudelevel and the largest negative amplitude level.
 6. The method of claim1, further comprising: assigning, to each amplitude level of themodulation scheme, a binary number; and for each message element,determining which binary number corresponds to the message I-branchamplitude value and which binary number corresponds to the messageQ-branch amplitude value.
 7. The method of claim 1, further comprising:receiving or determining a predetermined ratio; determining, from thedemodulation reference, a first amplitude level of the modulationscheme; calculating, according to the predetermined ratio and the firstamplitude level of the modulation scheme, a second amplitude level ofthe modulation scheme; and calculating Namp-2 intermediate amplitudelevels of the modulation scheme by interpolating between the first andsecond amplitude levels of the modulation scheme.
 8. The method of claim7, wherein: the calculating the second amplitude level of the modulationscheme comprises multiplying or dividing the first amplitude level bythe predetermined ratio.
 9. The method of claim 1, wherein: themodulation scheme includes a largest positive amplitude level and alargest negative amplitude level; the demodulation reference comprisesexactly one reference element comprising two reference element branchesat 90 degrees phase relative to each other; one of the reference elementbranches is modulated according to the largest positive amplitude leveland the other reference element branch is modulated according to thelargest negative amplitude level; and the determining the Namp amplitudelevels comprises interpolating between the largest positive and largestnegative amplitude levels.
 10. The method of claim 1, furthercomprising: receiving a first demodulation reference and determining afirst set of Namp amplitude levels therefrom, the first demodulationreference preceding the message in time or in frequency; receiving asecond demodulation reference and determining a second set of Nampamplitude levels therefrom, the second demodulation reference followingthe message in time or in frequency; and calculating a third set of Nampamplitude levels by averaging the first and second sets of Nampamplitude levels.
 11. The method of claim 10, wherein: the averaging thefirst and second sets of amplitude levels comprises, for each messageelement, interpolating between the first and second sets of amplitudelevels according to a position of the message element.
 12. The method ofclaim 10, wherein the second demodulation reference is different fromthe first demodulation reference.
 13. Non-transitory computer-readablemedia in a wireless receiver containing instructions that when executedby a computing environment cause a method to be performed, the methodcomprising: receiving a first demodulation reference comprising exactlyone reference element, the reference element modulated according to apulse-amplitude modulation (“PAM”) modulation scheme, the modulationscheme comprising integer Namp amplitude levels including a largestpositive amplitude level and a largest negative amplitude level;determining, according to the first demodulation reference, a firstreference I-branch signal and a first reference Q-branch signal at 90degrees phase relative to the first reference I-branch signal;determining the largest positive amplitude level according to onesignal, of the first reference I-branch and Q-branch signals;determining the largest negative amplitude level according to the othersignal, of the first reference I-branch and Q-branch signals; anddetermining at least one additional amplitude level by interpolatingbetween the largest positive and negative amplitude levels.
 14. Themedia of claim 13, the method further comprising: receiving a messagecomprising message elements, each message element modulated according tothe same modulation scheme as the reference element; and for eachmessage element: determining a message I-branch signal, and determining,from the message I-branch signal, a message I-branch amplitude, anddetermining which of the Namp amplitude levels is closest to the messageI-branch amplitude; and determining a message Q-branch signal at 90degrees phase relative to the message I-branch signal, and determining,from the message Q-branch signal, a message Q-branch amplitude; anddetermining which of the Namp amplitude levels is closest to the messageQ-branch amplitude.
 15. The media of claim 13, the method furthercomprising: receiving a second demodulation reference comprising exactlyone reference element; determining, according to the second demodulationreference, a second reference I-branch signal and a second referenceQ-branch signal; determining, according to the second reference I-branchsignal and the second reference Q-branch signal, a second largestpositive amplitude level and a second largest negative amplitude levelof the modulation scheme; determining a third largest positive amplitudelevel by combining the first and second largest positive amplitudelevels, and determining a third largest negative amplitude level bycombining the first and second largest negative amplitude levels;calculating the Namp amplitude levels of the modulation scheme byinterpolating between the third largest positive amplitude level and thethird largest negative amplitude level; receiving a message; anddemodulating the message according to the Namp amplitude levels of themodulation scheme.
 16. The media of claim 15, wherein: the firstreference I-branch signal is modulated according to the first largestpositive amplitude and the first reference Q-branch signal is modulatedaccording to the first largest negative amplitude level; and the secondreference I-branch signal is modulated according to the second largestnegative amplitude and the second reference Q-branch signal is modulatedaccording to the second largest positive amplitude level.
 17. The mediaof claim 16, wherein: one of the first and second demodulationreferences is positioned before the message in time or in frequency, andthe other of the first and second demodulation references is positionedafter the message in time or in frequency.
 18. A wireless communicationdevice configured to: receive a demodulation reference comprisinginteger Nref resource elements, Nref greater than 1 and less than 5,each resource element modulated according to a pulse-amplitudemodulation (“PAM”) modulation scheme, the modulation scheme comprisinginteger Namp amplitude levels; determine, according to the Nrefreference elements, Nref I-branch signals and Nref Q-branch signals, theQ-branch signals offset by 90 degrees in phase from the I-branchsignals; determine, according to the Nref I-branch signals and the NrefQ-branch signals, a plurality of the amplitude levels of the modulationscheme; determine, from the plurality of the amplitude levels sodetermined, one or more additional amplitude levels of the modulationscheme; receive a message comprising message elements modulatedaccording to the PAM modulation scheme, each message element comprisinga message I-branch amplitude value and a message Q-branch amplitudevalue; and compare each message I-branch amplitude value and eachmessage Q-branch amplitude value to the Namp amplitude levels of themodulation scheme, and therein determine which amplitude level, of theNamp amplitude levels of the modulation scheme, most closely matcheseach message I-branch amplitude value and each message Q-branchamplitude value.
 19. The device of claim 18, wherein either: themodulation scheme is 16QAM (quadrature amplitude modulation with 16states), Nref equals 2, and the Nref I-branch amplitude levels and theNref Q-branch amplitude levels comprise all of the Namp amplitude levelsof the modulation scheme; or the modulation scheme is 64QAM, Nref equals4, and the Nref I-branch amplitude levels and the Nref Q-branchamplitude levels comprise all of the Namp amplitude levels of themodulation scheme; or the modulation scheme is 256QAM, Nref equals 2,and the Nref I-branch amplitude levels and the Nref Q-branch amplitudelevels comprise the largest positive amplitude level, the smallestpositive amplitude level, the largest negative amplitude level, and thesmallest negative amplitude level, of the modulation scheme.
 20. Thedevice of claim 18, wherein: the message includes, embedded at one ormore predetermined locations, one or more interior demodulationreferences, each interior demodulation reference comprising exactly onereference element, the exactly one reference element comprising twobranch signals at 90 degrees phase relative to each other, the twobranch signals modulated according to the largest positive amplitudelevel and the largest negative amplitude level of the modulation scheme,respectively.